UC-NRLF 


B    M 


.IBRARY 

NIVERSITY  OF 
CAUFOflNIA 


PHYSICS  LIBRARY 


THE    CORPUSCULAR   THEORY 
OF    MATTER 


BY   THE    SAME   AUTHOR. 

THE  DISCHARGE    OF    ELECTRICITY  THROUGH 
GASES. 

Crown  8vo.    4/6  net. 

ELECTRICITY  AND  MATTER. 

Price  5/-  net. 


ARCHIBALD    CONSTABLE    &    CO.    LTD. 


THE   CORPUSCULAR 

THEORY    OF   MATTER 


BY 


J    }.  THOMSON,  M.A.   F  R.S.    D.Sc.  LL.D.  Ph.D. 

n 

PROFESSOR    OF    EXPERIMENTAL   PHYSICS,    CAMBRIDGE,    AND    PROFESSOR 
OF     NATURAL     PHILOSOPHY     AT     THE      ROYAL     INSTITUTION,      LONDON. 


NEW  YORK 

CHARLES   SCRIBNER'S   SONS 

1907 


f      I 


PREFACE 


THIS  book  is  an  expansion  of  a  course  of  lectures  given  at 
the  Koyal  Institution  in  the  Spring  of  1906.  It  contains  a 
description  of  the  properties  of  corpuscles  and  their 
application  to  the  explanation  of  some  physical  phenomena. 
In  the  earlier  chapters  a  considerable  amount  of  attention 
is  devoted  to  the  consideration  of  the  theory  that  many 
oe  the  properties  of  metals  are  due  to  the  motion  of 
corpuscles  diffused  throughout  the  metal.  This  theory  has 
received  strong  support  from  the  investigations  of  Drude 
and  Lorentz  ;  the  former  has  shown  that  the  theory  gives  an 
approximately  correct  value  for  the  ratio  of  the  thermal 
and  electrical  conductivities  of  pure  metals  and  the  latter 
that  it  accounts  for  the  long-wave  radiation  from  hot 
bodies.  I  give  reasons  for  thinking  that  the  theory  in  its 
usual  form  requires  the  presence  of  so  many  corpuscles 
that  their  specific  heat  would  exceed  the  actual  specific  heat 
of  the  metal.  I  have  proposed  a  modification  of  the  theory 
which  is  not  open  to  this  objection  and  which  makes  the 
ratio  of  the  conductivities  and  the  long-wave  radiation  of 
the  right  magnitude. 

The  later  chapters  contain  a  discussion  of  the  properties 
of  an  atom  built  up  of  corpuscles  and  of  positive  electricity, 
the  positive  electricity  being  supposed  to  occupy  a  much 
larger  volume  than  the  corpuscles.  The  properties  of  an 
atom  of  this  kind  are  shown  to  resemble  in  many  respects 
those  of  the  atoms  of  the  chemical  elements.  I  think  that  a 
theory  which  enables  us  to  picture  a  kind  of  model  atom 
and  to  interpret  chemical  and  physical  results  in  terms  of 

224555 


vi  PEEFACE. 

such  model  may  be  useful  even  though  the  models  are 
crude,  for  if  we  picture  to  ourselves  how  the  model  atom 
must  be  behaving  in  some  particular  physical  or  chemical 
process,  we  not  only  gain  a  very  vivid  conception  of  the 
process,  but  also  often  suggestions  that  the  process  under 
consideration  must  be  connected  with  other  processes,  and 
thus  further  investigations  are  promoted  by  this  method ;  it 
also  has  the  advantage  of  emphasising  the  unity  of  chemical 
and  electrical  action. 

In  Chapter  VII.  I  give  reasons  for  thinking  that  the 
number  of  corpuscles  in  an  atom  of  an  element  is  not 
greatly  in  excess  of  the  atomic  weight  of  the  element,  thus 
in  particular  that  the  number  of  corpuscles  in  an  atom  of 
hydrogen  is  not  large.  Some  writers  seem  to  think  that 
this  makes  the  conception  of  the  model  atom  more  difficult. 
I  am  unable  to  follow  this  view ;  it  seems  to  me  to  make 
the  conception  easier,  since  it  makes  the  number  of 
possible  atoms  much  more  nearly  equal  to  the  number  of 
the  chemical  elements.  It  has,  however,  an  important 
bearing  on  our  conception  of  the  origin  of  the  mass  of  the 
atom,  as  if  the  number  of  corpuscles  in  the  atom  is  of  the 
same  order  as  the  atomic  weight  we  cannot  regard  the 
mass  of  an  atom  as  mainly  or  even  appreciably  due  to  the 
mass  of  the  corpuscles. 

I  am  indebted  to  Mr.  G.  W.  C.  Kaye  for  assisting  in 
revising  the  proof  sheets. 


J.  J.  THOMSON. 


CAMBRIDGE, 

July  }->,  1907. 


CONTENTS 


CHAP.  PACK 

I.     INTRODUCTION— CORPUSCLES  IN  VACUUM  TUBES  1 


II.  THE  ORIGIN  OF  THE  MASS  OF  THE  CORPUSCLE      .        .  28 

III.  PROPERTIES  OF  A  CORPUSCLE  .                         ...  43 

IV.  CORPUSCULAR  THEORY  OF  METALLIC  CONDUCTION        .  49 
V.  THE  SECOND  THEORY  OF  ELECTRICAL  CONDUCTION      .  86 

VI.  THE  ARRANGEMENT  OF  CORPUSCLES  IN  THE  ATOM      .  103 

VII.  ON  THE  NUMBER  OF  CORPUSCLES  IN  AN  ATOM    .         .  142 


INDEX       .  ^  .  ....     169 


THE 

CORPUSCULAR     THEORY 
OF    MATTER 


CHAPTEE  I. 

THE  theory  of  the  constitution  of  matter  which  I  propose 
to  discuss  in  these  lectures,  is  one  which  supposes  that  the 
various  properties  of  matter  may  be  regarded  as  arising 
from  electrical  effects.  The  basis  of  the  theory  is  electricity, 
and  its  object  is  to  construct  a  model  atom,  made  up  of 
specified  arrangements  of  positive  and  negative  electricity, 
which  shall  imitate  as  far  as  possible  the  properties  of  the 
real  atom.  We  shall  postulate  that  the  attractions  and 
repulsions  between  the  electrical  charges  in  the  atom  follow 
the  familiar  law  of  the  inverse  square  of  the  distance, 
though,  of  course,  we  have  only  direct  experimental  proof 
of  this  law  when  the  magnitude  of  the  charges  and  the 
distances  between  them  are  enormously  greater  than  those 
which  can  occur  in  the  atom.  We  shall  not  attempt  to  go 
behind  these  forces  and  discuss  the  mechanism  by  which 
they  might  be  produced.  The  theory  is  not  an  ultimate 
one ;  its  object  is  physical  rather  than  metaphysical.  From 
the  point  of  view  of  the  physicist,  a  theory  of  matter  is  a 
policy  rather  than  a  creed ;  its  object  is  to  connect  or 
co-ordinate  apparently  diverse  phenomena,  and  above  all 
to  suggest,  stimulate  and  direct  experiment.  It  ought  to 
furnish  a  compass  which,  if  followed,  will  lead  the  observer 
further  and  further  into  previously  unexplored  regions. 

T.M.  B 


2     THE  .CORPUSCULAR   THEORY   OF   MATTER. 

Whether  these  regions  will  be  barren  or  fertile  experience 
alone  will  decide ;  but,  at  any  rate,  one  who  is  guided  in 
this  way  will  travel  onward  in  a  definite  direction,  and  will 
not  wander  aimlessly  to  and  fro. 

The  corpuscular  theory  of  matter  with  its  assumptions  of 
electrical  charges  and  the  forces  between  them  is  not  nearly 
so  fundamental  as  the  vortex  atom  theory  of  matter,  in 
which  all  that  is  postulated  is  an  incompressible,  friction- 
less  liquid  possessing  inertia  and  capable  of  transmitting 
pressure.  On  this  theory  the  difference  between  matter 
and  non-matter  and  between  one  kind  of  matter  and 
another  is  a  difference  between  the  kinds  of  motion  in  the 
incompressible  liquid  at  various  places,  matter  being  those 
portions  of  the  liquid  in  which  there  is  vortex  motion. 
The  simplicity  of  the  assumptions  of  the  vortex  atom  theory 
are,  however,  somewhat  dearly  purchased  at  the  cost  of  the 
mathematical  difficulties  which  are  met  with  in  its  develop- 
ment ;  and  for  many  purposes  a  theory  whose  consequences 
are  easily  followed  is  preferable  to  one  which  is  more 
fundamental  but  also  more  unwieldy.  We  shall,  however, 
often  have  occasion  to  avail  ourselves  of  the  analogy  which 
exists  between  the  properties  of  lines  of  electric  force  in  the 
electric  field  and  lines  of  vortex  motion  in  an  incompressible 
fluid. 

To  return  to  the  corpuscular  theory.  This  theory,  as  I 
have  said,  supposes  that  the  atom  is  made  up  of  positive 
and  negative  electricity.  A  distinctive  feature  of  this 
theory — the  one  from  which  it  derives  its  name — is  the 
peculiar  way  in  which  the  negative  electricity  occurs  both  in 
the  atom  and  when  free  from  matter.  We  suppose  that  the 
negative  electricity  always  occurs  as  exceedingly  fine  par- 
ticles called  corpuscles,  and  that  all  these  corpuscles,  when- 
ever they  occur,  are  always  of  the  same  size  and  always  carry 
the  same  quantity  of  electricity.  Whatever  may  prove  to 
be  the  constitution  of  the  atom,  we  have  direct  experi- 
mental proof  of  the  existence  of  these  corpuscles,  and  I  will 
begin  the  discussion  of  the  corpuscular  theory  with  a 
description  of  the  discovery  and  properties  of  corpuscles. 


CORPUSCLES  IN  VACUUM  TUBES. 


CORPUSCLES  IN  VACUUM  TUBES. 

The  first  place  in  which  corpuscles  were  detected  was  a 
highly  exhausted  tube  through  which  an  electric  discharge 
was  passing.  When  I  send  an  electric  discharge  through 
this  highly  exhausted  tube  you  will  notice  that  the  sides  of 
the  tube  glow  with  a  vivid  greeYi  phosphorescence.  That 
this  is  due  to  something  proceeding  in  straight  lines  from 
the  cathode — the  electrode  where  the  negative  electricity 
enters  the  tube  —  can  be  shown  in  the  following  way  : 
the  experiment  is  one  made  many  years  ago  by  Sir  William 
Crookes.  A  Maltese  cross  made  of  thin  mica  is  placed 
between  the  cathode  and  the  walls  of  the  tube.  You  will 
notice  that  when  I  send  the  discharge  through  the  tube, 
the  green  phosphorescence  does  not  now  extend  all  over 
the  end  of  the  tube  as  it  did  in  the  tube  without  the  cross. 
There  is  a  well-defined  cross  in  which  there  is  no  phos- 
phorescence at  the  end  of  the  tube ;  the  mica  cross  has 
thrown  a  shadow  on  the  tube,  and  the  shape  of  the  shadow 
proves  that  the  phosphorescence  is  due  to  something, 
travelling  from  the  cathode  in  straight  lines,  which  is 
stopped  by  a  thin  plate  of  mica.  The  gr^en  phosphorescence 
is  caused  by  cathode  rays,  and  at  one  time  there  was  a  keen 
controversy  as  to  the  nature  of  these  rays.  Two  views 
were  prevalent,  one,  which  was  chiefly  supported  by 
English  physicists,  was  that  the  rays  are  negatively  electri- 
fied bodies  shot  off  from  the  cathode  with  great  velocity ; 
the  other  view,  which  was  held  by  the  great  majority  of 
German  physicists,  was  that  the  rays  are  some  kind  of 
ethereal  vibrations  or  waves. 

The  arguments  in  favour  of  the  rays  being  negatively 
charged  particles  are  (1)  that  they  are  deflected  by 
a  magnet  in  just  the  same  way  as  moving  negatively 
electrified  particles.  We  know  that  such  particles  when 
a  magnet  is  placed  near  them  are  acted  upon  by  a 
force  whose  direction  is  at  right  angles  to  the  magnetic 
force,  and  also  at  right  angles  to  the  direction  in  which  the 
particles  are  moving.  Thus,  if  the  particles  are  moving 

B2 


4  THE  CORPUSCULAR  THEORY  OF  MATTER. 

horizontally  from  east  to  west,  and  the  magnetic  force  is 
horizontal  and  from  north  to  south,  the  force  acting  on  the 
negatively  electrified  particles  will  be  vertical  and  down- 
wards. 

When  the  magnet  is  placed  so  that  the  magnetic  force  is 
along  the  direction  in  which  the  particle  is  moving  the 
latter  will  not  be  affected  by  the  magnet.  By  placing  the 
magnet  in  suitable  positions  I  can  show  you  that  the 
cathode  particles  move  in  the  way  indicated  by  the  theory. 
The  observations  that  can  be  made  in  lecture  are  neces- 
sarily very  rough  and  incomplete;  but  I  may  add  that 
elaborate  and  accurate  measurements  of  the  movement  of 


FIG.  1. 


cathode  rays  under  magnetic  forces  have  shown  that  in  this 
respect  the  rays  behave  exactly  as  if  they  were  moving 
electrified  particles. 

The  next  step  made  in  the  proof  that  the  rays  are  nega- 
tively charged  particles,  was  to  show  that  when  they  are 
caught  in  a  metal  vessel  they  give  up  to  it  a  charge  of 
negative  electricity.  This  was  first  done  by  Perrin.  I 
have  here  a  modification  of  his  experiment.  A  is  a  metal 
cylinder  with  a  hole  in  it.  It  is  placed  so  as  to  be  out  of 
the  way  of  the  rays  coming  from  C,  unless  they  are  deflected 
by  a  magnet,  and  is  connected  with  an  electroscope.  You 
see  that  when  the  rays  do  not  pass  through  the  hole  in  the 
cylinder  the  electroscope  does  not  receive  a  charge.  I  now, 
by  means  of  a  magnet,  deflect  the  rays  so  that  they  pass 
through  the  hole  in  the  cylinder.  You  see  by  the  divergence 


COEPUSCLES   IN   VACUUM  TUBES.  5 

of  the  gold-leaves  that  the  electroscope  is  charged,  and  on 
testing  the  sign  of  the  charge  we  find  that  it  is  negative. 


DEFLECTION  OF  THE  KAYS  BY  A  CHARGED  BODY. 

If  the  rays  are  charged  with  np.gflifr'vft  plpptriVity 
ought  to  bedeflected  by  an  electrified  hnrly  «•«  wp.11  a.  a  by  a 
magnet.  In  the  earlier  experiments  made  on  this  point  no 
such  deflection  was  observed.  The  reason  of  this  has  been 
shown  to  be  that  when  the  cathode  rays  pass  through  a  gas 
they  make  it  a  conductor  of  electricity,  so  that  if  there  is 
any  appreciable  quantity  of  gas  in  the  vessel  through 


FIG.  2. 

which  the  rays  are  passing,  this  gas  will  become  a  con- 
ductor of  electricity,  and  the  rays  will  be  surrounded  by  a 
conductor  which  will  screen  them  from  the  effects  of 
electric  force  just  as  the  metal  covering  of  an  electroscope 
screens  off  all  external  electric  effects.  By  exhausting  the 
vacuum  tube  until  there  was  only  an  exceedingly  small 
quantity  of  air  left  in  to  be  made  a  conductor,  I  was  able 
to  get  rid  of  this  effect  and  to  obtain  the  electric  deflec- 
tion of  the  cathode  rays.  The  arrangement  I  used  for  this 
purpose  is  shown  in  Fig.  2.  The  rays  on  their  way  through 
the  tube  pass  between  two  parallel  plates,  A,  B,  which  can  be 
connected  with  the  poles  of  a  battery  of  storage  cells.  The 
pressure  in  the  tube  is  very  low.  You  will  notice  that  the 
rays  are  very  considerably  deflected  when  I  connect  the 
plates  with  the  poles  of  the  battery,  and  that  the  direction 


6  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

of   the   deflection   shows    that    the    rays    are    negatively 
charged. 

We  can  also  show  the  effect  of  magnetic  and  electric  force 
on  these  rays  if  we  avail  ourselves  of  the  discovery  made  by 
Wehnelt,  that  lime  when  raised  to  a  red  heat  emits  when 
negatively  charged  large  quantities  of  cathode  rays.  I  have 
here  a  tube  whose  cathode  is  a  strip  of  platinum  on  which 
there  is  a  speck  of  lime.  When  the  piece  of  platinum  is 
made  very  hot,  a  potential  difference  of  100  volts  or  so  is 
sufficient  to  make  a  stream  of  cathode  rays  start  from  this 
speck ;  you  will  be  able  to  trace  the  course  of  the  rays  by 
the  luminosity  they  produce  as  they  pass  through  the  gas. 


FIG.  3. 

You  can  see  the  rays  as  a  thin  line  of  bluish  light  coming 
from  a  point  on  the  cathode ;  on  bringing  a  magnet  near  it 
the  line  becomes  curved,  and  I  can  bend  it  into  a  circle  or  a 
spiral,  and  make  it  turn  round  and  go  right  behind  the 
cathode  from  which  it  started.  This  arrangement  shows 
in  a  very  striking  way  the  magnetic  deflection  of  the  rays. 
To  show  the  electrostatic  deflection  I  use  the  tube  shown  in 
Fig.  3.  I  charge  up.  the  plate  B  negatively  so  that  it  repels 
the  pencil  of  rays  which  approach  it  from  the  spot  of  lime  on 
the  cathode,  C.  You  see  that  the  pencil  of  rays  is  deflected 
from  the  plate  and  pursues  a  curved  path  whose  distance 
from  the  plate  I  can  increase  or  diminish  by  increasing  or 
diminishing  the  negative  charge  on  the  plate. 


COKPUSCLES  IN   VACUUM  TUBES.  7 

We  have  seen  that  the  cathode  rays  behave  under  every 
test  that  we  have  applied  as  if  they  are  negatively  elec- 
trified particles ;  we  have  seen  that  they  carry  a  negative 
charge  of  electricity  and  are  deflected  by  electric  and 
magnetic  forces  just  as  negatively  electrified  particles 
would  be. 

Hertz  showed,  however,  that  the  cathode  particles  possess 
another  property  which  seemed  inconsistent  with  the  idea 
that  they  are  particles  of  matter,  for  he  found  that  they 
were  able  to  penetrate  very  thin  sheets  of  metal,  for 
example,  pieces  of  gold-leaf  placed  between  them  and  the 
glass,  and  produce  appreciable  luminosity  on  the  glass  after 
doing  so.  The  idea  of  particles  as  large  as  the  molecules  of 
a  gas  passing  through  a  solid  plate  was  a  somewhat  startling 


FIG.  4. 

one  in  an  age  which  knew  not  radium — which  does  project 
.particles  of  this  size  through  pieces  of  metal  much  thicker 
than  gold-leaf — and  this  led  me  to  investigate  more  closely 
the  nature  of  the  particles  which  form  the  cathode  rays. 

The  principle  of  the  method  used  is  as  follows  :  When  a 
particle  carrying  a  charge  e  is  moving  with  the  velocity  v 
across  the  lines  of  force  in  a  magnetic  field,  placed  so  that 
the  lines  of  magnetic  force  are  at  right  angles  to  the  motion 
of  the  particle,  then  if  H  is  the  magnetic  force,  the 
moving  particle  will  be  acted  on  by  a  force  equal  to  He  v. 
This  force  acts  in  the  direction  which  is  at  right  angles  to 
the  magnetic  force  and  to  the  direction  of  motion  of  the 
particle,  so  that  if  the  particle  is  moving  horizontally  as  in 
the  figure  and  the  magnetic  force  is  at  right  angles  to  the 
plane  of  the  paper  and  towards  the  reader,  then  the  negatively 


8  THE  COEPUSCULAR  THEORY  OF  MATTER. 

electrified  particle  will  be  acted  on  by  a  vertical  and  upward 
force.  The  pencil  of  rays  will  therefore  be  deflected  upwards 
and  with  it  the  patch  of  green  phosphorescence  where  it 
strikes  the  walls  of  the  tube.  Let  now  the  two  parallel  plates 
A  and  B  (Fig.  2)  between  which  the  pencil  of  rays  is  moving 
be  charged  with  electricity  so  that  the  upper  plate  is  nega- 
tively and  the  lower  plate  positively  electrified,  the  cathode 
rays  will  be  repelled  from  the  upper  plate  with  a  force  Xe 
Or  where  X  is  the  electric  force  between  the  plates.  Thus,  if  the 
plates  are  charged  when  the  magnetic  field  is  acting  on  the 
rays,  the  magnetic  force  will  tend  to  send  the  rays  upwards, 
while  the  charge  on  the  plates  will  tend  to  send  them  down- 
wards. We  can  adjust  the  electric  and  magnetic  forces 
until  they  balance  and  the  pencil  of  rays  passes  horizon- 
tally in  a  straight  line  between  the  plates,  the  green  patch 
of  phosphorescence  being  undisturbed.  When  this  is  the 
case,  the  force  He  v  due  to  the  magnetic  field  is  equal  to 
Xe — the  force  due  to  the  electric  field — and  we  have 

He  v  =  Xe 
or       >=J 

Thus,  if  we  measure,  as  we  can  without  difficulty,  the 
values  of  X  and  H  when  the  rays  are  not  deflected,  we  can 
determine  the  value  of  r,  the  velocity  of  the  particles.  The 
velocity  of  the  rays  found  in  this  way  is  very  great ;  it 
varies  largely  with  the  pressure  of  the  gas  left  in  the  tube. 
In  a  very  highly  exhausted  tube  it  may  be  1/3  the  velocity  of 
light  or  about  60,000  miles  per  second  ;  in  tubes  not  so 
highly  exhausted  it  may  not  be  more  than  5,000  miles  per 
second,  but  in  all  cases  when  the  cathode  rays  are  produced 
in  tubes  their  velocity  is  much  greater  than  the  velocity  of 
any  other  moving  body  with  which  we  are  acquainted.  It 
is,  for  example,  many  thousand  times  the  average  velocity 
with  which  the  molecules  of  hydrogen  are  moving  at 
ordinary  temperatures,  or  indeed  at  any  temperature  yet 
realised. 


COEPUSCLES   IN   VACUUM  TUBES.  9 

DETERMINATION  OF  e/m. 

Having  found  the  velocity  of  the  rays,  let  us  in  the  pre- 
ceding experiment  take  away  the  magnetic  force  and  leave 
the  rays  to  the  action  of  the  electric  force  alone.  Then  the 
particles  forming  the  rays  are  acted  upon  by  a  constant 
vertical  downward  force  and  the  problem  is  practically  that 
of  a  bullet  projected  horizontally  with  a  velocity  v  and  fall- 
ing under  gravity.  We  know  that  in  time  t  the  body  will 
fall  a  depth  equal  to  J  g  t2  where  g  is  the  vertical  accelera- 
tion ;  in  our  case  the  vertical  acceleration  is  equal  to  X  e/m 
where  m  is  the  mass  of  the  particle,  the  time  it  is  falling 
is  l/v  where  I  is  the  length  of  path  measured  horizontally,  - 
and  v  the  velocity  of  projection.  Thus,  the  depth  the 
particle  has  fallen  when  it  reaches  the  glass,  i.e.,  the  down- 
ward displacement  of  the  patch  of  phosphorescence  where 
the  rays  strike  the  glass,  is  equal  to  ^ 

1  XeP 

2  m  v* 

We  can  easily  measure  d  the  distance  the  phosphorescent 
patch  is  lowered,  and  as  we  have  found  v  and  X  and  /  are 
easily  measured,  we  can  find  e/m  from  the  equation  : 


_ 
m        XL2 

The  results  of  the  determinations  of  the  values  of  e/m 
made  by  this  method  are  very  interesting,  for  it  is  found 
that  however  the  cathode  rays  are  produced  we  always 
get  the  same  value  of  e/m  for  all  the  particles  in  the 
rays.  We  may,  for  example,  by  altering  the  shape  of  the 
discharge  tube  and  the  pressure  of  the  gas  in  the  tube,  pro- 
duce great  changes  in  the  velocity  of  the  particles,  but  unless 
the  velocity  of  the  particles  becomes  so  great  that  they  are 
moving  nearly  as  fast  as  light,  when,  as  we  shall  see,  other 
considerations  have  to  be  taken  into  account,  the  value  of 
e/m  is  constant.  The  value  of  e/m  is  not  merely  inde- 
pendent of  the  velocity.  What  is  even  more  remarkable  is 
that  it  is  independent  of  the  kincLoL  electrodes  we  use  and 


10     THE   COEPUSCULAIl    THEOEY  OF   MATTES. 

also  of  the  kind  of  gas  in  the  tube.  The  particles  which 
form  the  cathode  rays  must  come  either  from  the  gas  in  the 
tube  or  from  the  electrodes ;  we  may,  however,  use  any 
kind  of  substance  we  please  for  the  electrodes  and  fill  the 
tube  with  gas  of  any  kind,  and  yet  the  value  of  e/m  will 
remain  unaltered. 

This  constant  value  is,  when  we  measure  e/m  in  the 
C.  G.  S.  system  of  magnetic  units,  equal  to  about  1*7  x  107. 
If  we  compare  this  with  the  value  of  the  ratio  of  the  mass 
to  the  charge  of  electricity  carried  by  any  system  previously 
known,  we  find  that  it  is  of  quite  a  different  order  of  magni- 
tude. Before  the  cathode  rays  were  investigated  the  charged 
atom  of  hydrogen  met  with  in  the  electrolysis  of  liquids 
was  the  system  which  had  the  greatest  known  value  for 
e/m,  and  in  this  case  the  value  is  only  104 ;  hence  for  the 
corpuscle  in  the  cathode  rays  the  value  of  e/m  is  1,700  times 
the  value  of  the  corresponding  quantity  for  the  charged 
hydrogen  atom.  This  discrepancy  must  arise  in  one  or 
other  of  two  ways,  either  the  mass  of  the  corpuscle  must  be 
very  small  compared  with  that  of  the  atom  of  hydrogen, 
which  until  quite  recently  was  the  smallest  mass  recognised 
in  physics,  or  else  the  charge  on  the  corpuscle  must  be  very 
much  greater  than  that  on  the  hydrogen  atom.  Now  it  has 
been  shown  by  a  method  which  I  shall  shortly  describe  that 
the  electric  charge  is  practically  the  same  in  the  two  cases ; 
hence  we  are  driven  to  the  conclusion  that  the  mass  of  the 
corpuscle  is  only  about  1/1700  of  that  of  the  hydrogen 
atom.  Thus  the  atom  is  not  the  ultimate  limit  to  the  sub- 
division of  matter ;  we  may  go  further  and  get  to  the 
corpuscle,  and  at  this  stage  the  corpuscle  is  the  same  from 
whatever  source  it  m#y  be  derived. 

CORPUSCLES  VERY  WIDELY  DISTRIBUTED. 

It  is  not  only  from  what  may  be  regarded  as  a  somewhat 
artificial  and  sophisticated  source,  viz.,  cathode  rays,  that 
we  can  obtain  corpuscles.  When  once  they  had  been 
discovered  it  was  found  that  they  were  of  very  general 
occurrence.  They  are  given  out  by  metals  when  raised  to 


COEPUSCLES  IN  VACUUM  TUBES.     11 

a  red  heat :  you  have  already  seen  what  a  copious  supply 
is  given  out  by  hot  lime.  Any  substance  when  heated  gives 
out  corpuscles  to  some  extent ;  indeed,  we  can  detect  the 
emission  of  them  from  some  substances,  such  as  rubidium 
and  the  alloy  of  sodium  and  potassium,  even  when  they  are 
cold;  and  it  is  perhaps  allowable  to  suppose  that  there 
is  some  emission  by  all  substances,  though  our  instruments 
are  not  at  present  sufficiently  delicate  to  detect  it  unless  it 
is  unusually  large. 

Corpuscles  are  also  given  out  by  metals  and  other  bodies, 
but  especially  by  the  alkali  metals,  when  these  are  exposed 
to  light.  They  are  being  continually  given  out  in  large 
quantities,  and  with  very  great  velocities  by  radio-active 
substances  such  as  uranium  and  radium  ;  they  are  pro- 
duced in  large  quantities  when  salts  are  put  into  flames, 
and  there  is  good  reason  to  suppose  that  corpuscles  reach 
us  from  the  sun. 

The  corpuscle  is  thus  very  widely  distributed,  but  where- 
ever  it  is  found  it  preserves  its  individuality,  e/m  being 
always  equal  to  a  certain  constant  value. 

The  corpuscle  appears  to  form  a  part  of  all  kinds  of 
matter  under  the  most  diverse  conditions  ;  it  seems  natural, 
therefore,  to  regard  it  as  one  of  the  bricks  of  which  atoms 
are  built  up. 

MAGNITUDE  OF  THE  ELECTRIC  CHARGE  CARRIED  BY  THE 
CORPUSCLE. 

I  shall  now  return  to  the  proof  that  the  very  large  value 
of  e/m  for  the  corpuscle  as  compared  with  that  for  the  atom 
of  hydrogen  is  due  to  the  smallness  of  m  the  mass,  and  not 
to  the '  greatness  of  e  the  charge.  We  can  do  this  by 
actually  measuring  the  value  of  e,  availing  ourselves  for 
this  purpose  of  a  discovery  by  C.  T.  K.  Wilson,  that  a 
charged  particle  acts  as  a  nucleus  round  which  water 
vapour  condenses,  and  forms  drops  of  water.  If  we  have  air 
saturated  with  water  vapour  and  cool  it  so  that  it  would  be 
supersaturated  if  there  were  no  deposition  of  moisture,  we 
know  that  if  any  dust  is  present,  the  particles  of  dust  act 


12  THE  CORPUSCULAR  THEORY  OF  MATTER. 

as  nuclei  round  which  the  water  condenses  and  we  get  the 
too  familiar  phenomena  of  fog  and  rain.  If  the  air  is  quite 
dust-free  we  can,  however,  cool  it  very  considerably  without 
any  deposition  of  moisture  taking  place.  If  there  is  no 
dust,  C.  T.  E.  Wilson  has  shown  that  the  cloud  does  not 
form  until  the  temperature  has  been  lowered  to  such  a 
point  that  the  supersaturation  is  about  eightfold.  When, 
however,  this  temperature  is  reached,  a  thick  fog  forms, 
even  in  dust-free  air.  When  charged  particles  are  present 


FIG.  5, 

in  the  gas,  Wilson  showed  that  a  much  smaller  amount  of 
cooling  is  sufficient  to  produce  the  fog,  a  fourfold  super- 
saturation  being  all  that  is  required  when  the  charged 
particles  are  those  which  occur  in  a  gas  when  it  is  in  the 
state  in  which  it  conducts  electricity.  Each  of  the  charged 
particles  becomes  the  centre  round  which  a  drop  of  water 
forms ;  the  drops  form  a  cloud,  and  thus  the  charged  par- 
ticles, however  small  to  begin  with,  now  become  visible  and 
can  be  observed.  The  effect  of  the  charged  particles  on  the 
formation  of  a  cloud  can  be  shown  very  distinctly  by  the 


COEPUSCLES  IN  VACUUM  TUBES.     13 

following  experiment.     The  vessel  A,  which  is  in  contact 
with  water,  is  saturated  with  moisture  at  the  temperature 
of  the  room.     This  vessel  is  in  communication  with  B,  a 
cylinder  in  which  a  large  piston,  C,  slides  up  and  down ;  the 
piston,  to  begin  with,  is  at  the  top  of  its  travel ;  then  by 
suddenly  exhausting  the  air  from  below  the  piston,   the 
pressure  of  the  air  above  it  will  force  it  down  with  great 
rapidity,  and  the  air  in  the   vessel  A   will  expand   very 
quickly.     When,  however,  air  expands  it  gets  cool ;  thus  the 
air  in  A  gets  colder,  and  as  it  was  saturated  with  moisture 
before  cooling,  it  is  now  supersaturated.      If  there  is  no 
dust   present,  no   deposition  of   moisture  will  take   place 
unless  the  air  in  A  is  cooled  to  such  a  low  temperature  that 
the   amount  of   moisture   required  to  saturate  it  is  only 
about  1/8  of  that  actually  present.     Now  the  amount  of 
cooling,  and  therefore  of  supersaturation,  depends  upon  the 
travel  of  the  piston ;    the  greater  the  travel  the  greater  the 
cooling.      I  can  regulate  this  travel   so    that   the   super- 
saturation  is  less   than  eightfold,  and  greater   than  four- 
fold.    We  now  free  the  air  from  dust  by  forming  cloud  after 
cloud  in  the  dusty  air,  as  the  clouds  fall  they  carry  the 
dust  down  with  them,  just  as  in  nature  the  air  is  cleared  by 
showers.     We  find  at  last  that  when  we  make  the  expansion 
no  cloud  is  visible.     We  now  put  the  gas  in  a  conducting 
state  by  bringing  a  little  radium  near  the  vessel  A  ;  this  fills 
the  gas  with  large  quantities  of  both  positively  and  nega- 
tively electrified  particles.     On  making  the  expansion  now, 
an  exceedingly  dense  cloud  is  formed.     That  this  is  due  to 
the  electrification  in  the  gas  can  be  shown  by  the  following 
experiment:  Along  the  inside  walls  of  the  vessel  A  we  have  two 
vertical  insulated  plates  which  can  be  electrified;   if  these 
plates  are  electrified  they  will  drag  the  charged  particles  out 
of  the  gas  as  fast  as  they  are  formed,  so  that  by  electrifying 
the  plates  we  can  get  rid  of,  or  at  any  rate  largely  reduce, 
the  number  of  electrified  particles  in  the  gas.    I  now  repeat 
the  experiment,  electrifying  the  plates  before  bringing  up 
the  radium.    You  see  that  the  presence  of  the  radium  hardly 
increases  the  small  amount  of  cloud.     I  now  discharge  the 


14  THE  CORPUSCULAR  THEORY  OF  MATTER. 

plates,  and  on  making  the  expansion  the  cloud  is  so  dense 
as  to  be  quite  opaque. 

We  can  use  the  drops  to  find  the  charge  on  the  particles, 
for  when  we  know  the  travel  of  the  piston  we  can  deduce 
the  amount  of  supersaturation,  and  hence  the  amount  of 
water  deposited  when  the  cloud  forms.  The  water  is 
deposited  in  the  form  of  a  number  of  small  drops  all  of  the 
same  size ;  thus  the  number  of  drops  will  be  the  volume  of 
the  water  deposited  divided  by  the  volume  of  one  of  the 
drops.  Hence,  if  we  find  the  volume  of  one  of  the  drops 
we  can  find  the  number  of  drops  which  are  formed  round 
the  charged  particles.  If  the  particles  are  not  too  numerous, 
each  will  have  a  drop  round  it,  and  we  can  thus  find  the 
number  of  electrified  particles. 

If  we  observe  the  rate  at  which  the  drops  slowly  fall  down 
we  can  determine  the  size  of  the  drops.  In  consequence  of 
the  viscosity  or  friction  of  the  air  small  bodies  do  not  fall 
with  a  constantly  accelerated  velocity,  but  soon  reach  a  speecf 
which  remains  uniform  for  the  rest  of  the  fall ;  the  smaller 
the  body  the  slower  this  speed,  and  Sir  George  Stokes  has 
shown  that  v,  the  speed  at  which  a  drop  of  rain  falls,  is 
given  by  the  formula — 

2 \  go* 
=  9    /* 

where  a  is  the  radius  of  the  drop,  g  the  acceleration  due 
to  gravity,  and  ^  the  co -efficient  of  viscosity  of  the  air.  If 
we  substitute  the  values  of  g  and  /*,  we  get 

v  =  1-28  X  106  a" 

Hence,  if  we  measure  v  we  can  determine  a,  the  radius  of 
the  drop.  We  can,  in  this  way,  find  the  volume  of  a  drop, 
and  may  therefore,  as  explained  above,  calculate  the  number 
of  drops,  and  therefore  the  number  of  electrified  particles. 
It  is  a  simple  matter  to  find,  by  electrical  methods,  the  total 
quantity  of  electricity  on  these  particles;  and  hence,  as  we 
know  the  number  of  particles,  we  can  deduce  at  once  the 
charge  on  each  particle. 


COEPUSCLES  IN  VACUUM  TUBES.     15 

This  was  the  method  by  which  I  first  determined  the 
charge  on  the  particle.  H.  A.  Wilson  has  since  used  a 
simpler  method  founded  on  the  following  principles. 
C.  T.  K.  Wilson  has  shown  that  the  drops  of  water  condense 
more  easily  on  negatively  electrified  particles  than  on 
positively  electrified  ones.  Thus,  by  adjusting  the  expansion, 
it  is  possible  to  get  drops  of  water  round  the  negative 
particles  and  not  round  the  positive  ;  with  this  expansion, 
therefore,  all  the  drops  are  negatively  electrified.  The  size 
of  these  drops,  and  therefore  their  weight,  can,  as  before, 
be  determined  by  measuring  the  speed  at  which  they  fall 
under  gravity.  Suppose  now,  that  we  hold  above  the  drops 
a  positively  electrified  body,  then  since  the  drops  are 
negatively  electrified  they  will  be  attracted  towards  the 
positive  electricity  and  thus  the  downward  force  on  the 
drops  will  be  diminished,  and  they  will  not  fall  so  rapidly 
as  they  did  when  free  from  electrical  attraction.  If  we 
adjust  the  electrical  attraction  so  that  the  upward  force  on 
each  drop  is  equal  to  the  weight  of  the  drop,  the  drops  will 
not  fall  at  all,  but  will,  like  Mahomet's  coffin,  remain  sus- 
pended between  heaven  and  earth.  If,  then,  we  adjust  the 
electrical  force  until  the  drops  are  in  equilibrium  and  neither 
fall  nor  rise,  we  know  that  the  upward  force  on  the  drop  is 
equal  to  the  weight  of  the  drop,  which  we  have  already 
determined  by  measuring  the  rate  of  fall  when  the  drop 
was  not  exposed  to  any  electrical  force.  If  Xis  the  electrical 
force,  e  the  charge  on  the  drop,  and  w  its  weight,  we  have, 
when  there  is  equilibrium — 

X  e  =  w. 

Since  X  can  easily  be  measured,  and  w  is  known,  we  can 
use  this  relation  to  determine  e,  the  charge  on  the  drop. 
The  value  of  e  found  by  these  methods  is  3'1  X  10~10  electro- 
static units,  or  10~20  electromagnetic  units.  This  value  is 
the  same  as  that  of  the  charge  carried  by  a  hydrogen  atom 
in  the  electrolysis  of  dilute  solutions,  an  approximate  value 
of  which  has  long  been  known. 

It  might  be  objected  that  the  charge  measured  in  the 


16  THE  CORPUSCULAR  THEORY  OF  MATTER. 

preceding  experiments  is  the  charge  on  a  molecule  or 
collection  of  molecules  of  the  gas,  and  not  the  charge  on 
a  corpuscle.  This  objection  does  not,  however,  apply  to 
another  form  in  which  I  tried  the  experiment,  where  the 
charges  on  the  particles  were  got,  not  by  exposing  the  gas 
to  the  effects  of  radium,  but  by  allowing  ultra-violet  light  to 
fall  on  a  metal  plate  in  contact  with  the  gas.  In  this  case, 
as  experiments  made  in  a  very  high  vacuum  show,  the 
electrification  which  is  entirely  negative  escapes  from  the 
metal  in  the  form  of  corpuscles.  When  a  gas  is  present, 
the  corpuscles  strike  against  the  molecules  of  the  gas  and 
stick  to  them.  Thus,  though  it  is  the  molecules  which  are 
charged,  the  charge  on  a  molecule  is  equal  to  the  charge  on 
a  corpuscle,  and  when  we  determine  the  charge  on  the 
molecules  by  the  methods  I  have  just  described,  we  deter- 
mine the  charge  carried  by  the  corpuscle.  The  value  of  the 
charge  when  the  electrification  is  produced  by  ultra-violet 
light  is  the  same  as  when  the  electrification  is  produced  by 
radium. 

We  have  just  seen  that  e,  the  charge  on  the  corpuscle,  is 
in  electromagnetic  units,  equal  to  10~20,  and  we  have  pre- 
viously found  that  elm,  m  being  the  mass  of  a  corpuscle,  is 
equal  to  1/7  X  107,  hence  in  —  6  X  10~28  grammes. 

WTe  can  realise  more  easily  what  this  means  if  we  express 
the  mass  of  the  corpuscle  in  terms  of  the  mass  of  the  atom 
of  hydrogen.  We  have  seen  that  for  the  corpuscle 
e/m  =  1'7  X  107;  while  if  E  is  the  charge  carried  by  an 
atom  of  hydrogen  in  the  electrolysis  of  dilute  solutions,  and 
M  the  mass  of  the  hydrogen  atom,  E/M  —  104;  hence 
e/m  =  1700  E/M.  We  have  already  stated  that  the 
value  of  e  found  by  the  preceding  methods  agrees  well 
with  the  value  of  E,  which  has  long  been  approximately 
known.  Townsend  has  used  a  method  in  which  the  value 
of  e/E  is  directly  measured  and  has  showed  in  this  way  also 
that  e  is  equal  to  E  ;  hence,  since  e/m  =  1700  E/M,  we  have 
M  =  1700  m,  i.e.,  the  mass  of  a  corpuscle  is  only  about 
1/1700  part  of  the  mass  of  the  hydrogen  atom. 

In  all  known  cases  in  which  negative  electricity  occurs  in 


CORPUSCLES  IN  VACUUM  TUBES.     17 

gases  at  very  low  pressures  it  occurs  in  the  form  of 
corpuscles,  small  bodies  with  an  invariable  charge  and 
mass.  The  case  is  entirely  different  with  positive  electricity. 

THE  CARRIERS  OF  POSITIVE  ELECTRICITY. 

We  get  examples  of  positively  charged  particles  in  various 
phenomena.  One  of  the  first  cases  to  be  investigated  was 
that  of  the  "  Canalstrahlen  "  discovered  by  Goldstein.  I  have 
here  a  highly  exhausted  tube  with  a  cathode,  through 
which  a  large  number  of  holes  has  been  bored.  When  I 
send  a  discharge  through  this  tube  you  will  see  the  cathode 
rays  shooting  out  in  front  of  the  cathode.  In  addition  to 
these,  you  see  other  rays  streaming  through  the  holes  in 
the  cathode,  and  travelling  through  the  gas  at  the  back  of 


FIG.    6. 

the  cathode.  These  are  called  "  Canalstrahlen."  You  notice 
that,  like  the  cathode  rays,  they  make  the  gas  luminous  as 
they  pass  through  it,  but  the  colour  of  the  luminosity  due 
to  the  Canalstrahlen  is  not  the  same  as  that  due  to  the 
cathode  rays.  The  distinction  is  exceptionally  well  marked 
in  helium,  where  the  luminosity  due  to  the  Canalstrahlen  is 
tawny,  and  that  due  to  the  cathode  rays  bluish.  The 
luminosity,  too,  produced  when  the  rays  strike  against  a 
solid  is  also  of  quite  a  different  character.  This  is  well 
shown  by  allowing  both  cathode  rays  and  Canalstrahlen  to 
strike  against  lithium  chloride.  Under  the  cathode  rays 
the  salt  gives  out  a  steely  blue  light,  and  the  spectrum  is  a 
continuous  one ;  under  the  Canalstrahlen  the  salt  gives  out 
a  brilliant  red  light,  and  the  spectrum  shows  the  lithium 
line.  It  is  a  very  interesting  fact  that  the  lines  in  the 
spectra  of  the  alkali  metals  are  very  much  more  easily 
T.M.  c 


18  THE  CORPUSCULAR  THEORY  OF  MATTER. 

obtained  when  the  canalstrahlen  fall  on  salts  of  the  metal 
than  when  they  fall  on  the  metal  itself.  Thus  when  a  pool 
of  the  liquid  alloy  of  sodium  and  potassium  is  bombarded  by 
canalstrahlen  the  specks  of  oxide  on  the  surface  shine  with 
a  bright  yellow  light,  while  the  untarnished  part  of  the 
surface  is  quite  dark. 

The  canalstrahlen  are  deflected  by  a  magnet,  though  not 
to  anything  like  the  same  extent  as  the  cathode  rays.  Their 
deflection,  too,  is  in  the  opposite  direction,  showing  that 
they  are  positively  charged. 

VALUE  OF  e/m  FOE  THE  PARTICLES  IN  THE  CANALSTRAHLEN. 

W,  Wien  has  applied  the  methods  described  in  connection 
with  the  cathode  rays  to  determine  the  value  of  e/m  for  the 
particles  in  the  canalstrahlen.  The  contrast  between  the 
results  obtained  for  the  two  rays  is  very  interesting.  In 
the  case  of  the  cathode  rays  the  velocity  of  different  rays 
in  the  same  tube  may  be  different,  but  the  value  of  e/m  for 
these  rays  is  independent  of  the  velocity  as  well  as  of  the 
nature  of  the  gas  and  the  electrodes.  In  the  case  of  the 
canalstrahlen  we  get  in  the  same  pencil  of  rays  not  merely 
variations  in  the  velocity,  but  also  variations  in  the  value 
of  e/m.  The  difference  between  the  values  of  e/m  for  the 
cathode  rays  and  the  canalstrahlen  is  also  very  remarkable. 
For  the  cathode  rays  e/m  always  equal  to  1*7  X 107 ;  while 
for  canalstrahlen  the  greatest  value  ever  observed  is  104, 
which  is  also  the  value  of  e/m  for  the  hydrogen  ions  in  the 
electrolysis  of  dilute  solutions.  When  the  canalstrahlen 
pass  through  hydrogen  the  value  of  e/m  for  a  large  portion 
of  the  rays  is  104.  There  are,  however,  some  rays  present 
even  in  hydrogen,  for  which  e/m  is  much  less  than  104,  and 
which  are  but  slightly  deflected  even  -by  very  intense 
magnetic  fields.  When  the  canalstrahlen  pass  through 
very  pure  oxygen,  Wien  found  that  the  value  of  e/m  for 
the  most  conspicuous  rays  was  about  750,  which  is  not  far 
from  what  it  would  be  if  the  charge  were  the  same  as  for 
the  canalstrahlen  in  hydrogen,  while  the  mass  was  greater 
in  the  proportion  of  the  mass  of  an  atom  of  oxygen  to  that 


COEPUSCLES   IN   VACUUM   TUBES. 


19 


of  an  atom  of  hydrogen.  Along  with  these  rays  in  oxygen 
there  were  others  having  still  smaller  values  of  e/m,  and 
some  having  e/m  equal  to  104. 

As  the  canalstrahlen  or  rays  of  positive  electricity  are 
a  very  promising  field  for  investigations  on  the  nature 
of  positive  electricity,  I  have  recently  made  a  series  of 
experiments  on  these  rays  in  different  gases,  measuring 
the  deflections  they  experience  when  exposed  to  electric 
and  magnetic  forces  and  thus  deducing  the  values  of  e/m 
and  v.  I  find,  when  the  pressure  of  the  gas  is  not  too  low, 


FIG.  7. 

The  portions  with  the  cross  shading  is  the  deflection  under  both 
electric  and  magnetic  force  ;  the  portion  with  vertical  shading  the 
deflection  under  magnetic  force ;  that  with  the  horizontal  shading 
under  electric  force  alone. 

that  the  bright  spot  produced  by  the  impact  of  these 
rays  on  the  phosphorescent  screen  is  deflected  by  electric 
and  magnetic  forces  into  a  continuous  band  extending,  as 
shown  in  Fig.  7,  on  both  sides  of  the  undeflected  portion, 
the  portion  on  one  side  (cc)  is  very  much  fainter  than  that 
on  the  other,  and  also  somewhat  shorter.  The  direction 
of  the  deflection  of  the  band  cc  shows  that  it  is  produced 
by  particles  charged  with  negative  electricity,  while  the 
brighter  band  bb  is  due  to  particles  charged  with  positive 
electricity.  The  negatively  charged  particles  which  pro- 
duce the  band  cc  are  not  corpuscles,  for  from  the  deflections 
in  this  band  we  can  find  the  value  of  e/m ;  as  this  value 

c2 


20  THE  COEPUSCULAE  THEOEY  OF  MATTER. 

comes  out  of  the  order  104,  we  see  thpt  the  mass  of  the 
carrier  is  comparable  with  that  of  an  atom,  and  therefore 
immensely  greater  than  that  of  a  corpuscle.  When  the 
pressure  is  very  low  the  portion  of  the  phosphorescence 
deflected  in  the  negative  direction  disappears  and  the  phos- 
phorescent spot,  instead  of  being  stretched  by  the  electric 
and  magnetic  forces  into  a  continuous  band,  is  broken  up 
into  two  patches,  as  in  the  curved  parts  of  Figs.  8  and  9. 
Fig.  8  is  the  appearance  at  exceedingly  low  pressures,  Fig.  9 
that  at  a  somewhat  higher  pressure.  For  one  of  these  patches 
the  maximum  value  of  e/m  is  about  104,  and  for  the  other 
about  5  X 103.  The  appearance  of  the  patches  and  the  values 
of  ejm  at  these  very  low  pressures  are  the  same  whether 


00 
FIG.    8.  FIG.    9. 

The  curved  patches  represent  the 
deflection  under  both  electric 
and  magnetic  force. 


the  tube  is  filled  originally  with  air,  hydrogen,  or  helium. 
Another  experiment  I  tried  was  to  exhaust  the  tube  until 
the  pressure  was  too  low  for  the  discharge  to  pass,  and  then 
to  introduce  into  the  tube  a  very  small  quantity  of  gas,  this 
increases  the  pressure  and  the  discharge  is  able  to  pass 
through  the  tube.  The  following  gases  were  admitted  into 
the  tube:  air,  carbonic  oxide,  oxygen,  hydrogen,  helium, 
argon  and  neon,  but  whatever  the  gas  the  appearance  of  the 
phosphorescence  was  the  same.  In  every  case  there  were 
two  patches,  one  having  e/m  =  104,  the  other  e/m  =  5  X  10y. 
At  these  very  low  pressures  the  intensity  of  the  electric 
field  in  the  discharge  tube  is  very  great. 

When  the  pressure  in  the  tube  is  not  very  low  the  nature 
of  the  positive  rays  depends  to  a  very  considerable  extent 


COEPUSCLES  IN  VACUUM  TUBES.     21 

upon  the  kind  of  gas  with  which  the  tube  is  filled.  Thus, 
for  example,  in  air  at  these  pressures  the  phosphorescent 
spot  is  stretched  out  into  a  straight  band  as  in  Fig.  7 ;  the 
maximum  value  of  e/m  for  this  band  is  104.  In  hydrogen 
at  suitable  pressures  we  get  the  spot  stretched  out  into  two 
bands  as  in  Fig.  10 ;  for  one  of  these  bands  the  maximum 


FIG. 


value  of  e/m  is  104,  while  for  the  other  it  is  5  X  103.  In 
helium  we  also  get  two  bands  as  in  Fig.  11,  but  while  the 
maximum  value  of  e/m  in  one  of  these  bands  is  104,  the 
same  as  for  the  corresponding  band  in  hydrogen,  the 
maximum  value  of  e/m  in  the  other  band  is  only  2*5  X  103. 
We  see  from  this  that  the  ratio  of  the  masses  of  the  carriers 


FIG.    11. 

in  the  two  bands  is  equal  to  the  ratio  of  the  masses  of  the 
atoms  of  hydrogen  and  helium. 

At  some  pressures  we  get  three  bands  in  helium,  the 
value  of  e/m  being  respectively  104,  5  X  103,  and  2*5  X  108. 

The  continuous  band  into  which  the  bright  phosphorescent 
spot  is  stretched  out  when  the  pressure  is  not  exceedingly 
low  can  be  explained  as  follows : — 

The  rays  on  their  way  to  the  screen  have  to  pass 
through  gas  which  is  ionised  by  the  passage  through  it  of 


22  THE  COKPUSCULAE  THEORY  OF  MATTER. 

the  rays ;  this  gas  will  therefore  contain  free  corpuscles. 
The  particles  which  constitute  the  rays  start  with  a  charge 
of  positive  electricity ;  some  of  these  in  their  journey 
through  the  gas  may  attract  a  corpuscle,  the  negative 
charge  on  which  will  neutralise  the  positive  charge  on  the 
particle.  The  particles  when  in  this  neutral  state  may  be 
ionised  by  collision  and  reacquire  a  positive  charge,  or  by 
attracting  another  corpuscle  they  may  become  negatively 
charged,  and  this  process  may  be  repeated  several  times  in 
their  journey  to  the  screen.  Thus,  some  of  the  particles, 
instead  of  being  positively  charged  for  the  whole  of  the 
time  they  are  exposed  to  electric  and  magnetic  forces,  may 
be  for  a  part  of  that  time  without  a  charge  or  even  have  a 
negative  charge.  Now  the  deflection  of  a  particle  will  be 
proportional  to  the  average  value  of  its  charge  while 
under  the  action  of  electric  and  magnetic  forces ;  if  the 
particle  is  without  charge  for  a  part  of  the  time,  its  deflec- 
tion will  be  less  than  that  of  a  particle  which  has  retained 
its  positive  charge  for  the  whole  of  the  journey,  while  the 
small  number  of  particles,  which  have  a  negative  charge 
for  a  longer  time  than  they  have  a  positive,  will  be  deflected 
in  the  opposite  direction  and  produce  the  faint  tail  of 
phosphorescence  which  is  deflected  in  the  opposite  direction 
to  the  main  "portion. 

It  is  remarkable  and  suggestive  that  even  when  great 
care  is  taken  to  eliminate  hydrogen  from  the  tube,  we  get 
at  all  pressures  a  large  quantity  of  rays  for  which  e/m  is 
equal  to  104,  the  value  for  the  hydrogen  atom  ;  and  in 
many  cases  this  is  the  only  definite  value  of  e/m  to  be 
observed,  for  the  continuous  band  in  which  we  have  all 
Values  of  e/m  is  due,  as  we  have  seen,  not  to  changes  in  m, 
but  to  changes  in  the  average  value  of  e. 

If  the  presence  of  rays  for  which  e/m  =  104  was  entirely 
due  to  hydrogen  present  as  an  impurity  in  the  gas  with 
which  the  tube  is  filled,  the  positive  particles  being  hydrogen 
ionised  by  the  corpuscles  projected  from  the  cathode,  we 
should  have  expected,  since  the  ionisation  consists  in  the 
detachment  of  a  corpuscle  from  the  molecule,  that  the 


COEPUSCLES  IN  VACUUM  TUBES.     23 

positively  charged  particles  would  be  molecules  and  not 
atoms  of  hydrogen. 

Again,  at  very  low  pressures,  when  the  electric  field  is 
very  intense,  we  get  the  same  two  types  of  carriers  what- 
ever kind  of  gas  is  in  the  tube.  For  one  of  these  types 
e/m  =  104  and  for  the  other  e/m  =  5  X 103 ;  the  second  value 
corresponds  to  the  positive  particles  which  are  given  out  by 
radio-active  substances.  The  most  obvious  interpretation 
of  this  result  is  that  under  the  conditions  existing  in  the 
discharge  tube  at  these  very  low  pressures  all  gases  give 
off  positive  particles  which  resemble  corpuscles,  in  so  far 
as  they  are  independent  of  the  nature  of  the  gas  from 
which  they  are  derived,  but  which  differ  from  the  corpuscles 
in  having  masses  comparable  with  the  mass  of  an  atom  of 
hydrogen,  while  the  mass  of  a  corpuscle  is  only  1/1700  of 
this  mass.  One  type  of  positive  particle  has  a  mass  equal 
to  that  of  an  atom  of  hydrogen,  the  other  type  has  a  mass 
double  this ;  and  the  experiments  I  have  just  described 
indicate  that  when  the  pressure  is  very  low  and  the  electric 
field  very  intense,  all  the  positively  electrified  particles  are 
of  one  or  other  of  these  types. 

We  have  seen  that  for  the  positively  charged  particles 
in  the  canalstrahlen  the  value  of  e/m  depends,  when  the 
pressure  is  not  too  low,  on  the  kind  of  gas  in. the  tube,  and 
is  such  that  the  least  value  of  in  is  comparable  with  the 
mass  of  an  atom  of  hydrogen,  and  is  thus  always  immensely 
greater  than  the  carriers  of  the  negative  charge  in  the 
cathode  rays.  We  know  of  no  case  where  the  mass  of  the 
positively  charged  particle'  is  less  than  that  of  an  atom  of 
hydrogen. 

POSITIVE  IONS  FROM  HOT  WIRES. 

When  a  metallic  wire  is  raised  to  a  red  heat  it  gives  out 
positively  electrified  particles.  I  have  investigated  the 
values  of  e/m  for  these  particles,  and  find  that  they  show 
the  same  peculiarities  as  the  positively  charged  particles  in 
the  canalstrahlen.  The  particles  given  off  by  the  wire  are 
not  all  alike.  Some  have  one  value  of  e/m,  others  another, 


24  THE  COBPUSCULAR  THEORY  OF  MATTER. 

but  the  greatest  value  I  found  in  my  experiments  where 
the  wire  was  surrounded  by  air  .at  a  low  pressure  was  720, 
and  there  were  many  particles  for  which  e/m  was  very 
much  smaller,  and  which  were  hardly  affected  even  by  very 
strong  magnetic  fields. 

POSITIVE  IONS  FBOM  RADIO-ACTIVE  SUBSTANCES. 

The  various  radio-active  substances,  such  as  radium, 
polonium,  uranium,  and  actinium,  shoot  out  with  great 
velocity  positively  electrified  particles  which  are  called  ^rays. 
The  values  of  e/m  for  these  particles  have  been  measured  by 
Rutherford,  Des  Coudres,  Mackenzie,  and  Huff,  and  for  all 
the  substances  hitherto  examined — radium  and  its  trans- 
formation products,  polonium,  and  actinium — the  value  of 
e/m  is  the  same  and  equal  to  5  X  103,  the  same  as  for  one 
type  of  ray  in  the  vacuum  tube.  The  velocity  with  which 
the  particles  move  varies  considerably  from  one  substance 
to  another.  As  these  substances  all  give  off  helium,  there 
is  primd  Jade  evidence  that  the  a  particles  are  helium. 
For  a  helium  atom  with  a  single  charge,  e/m  is  2'5  X  103, 
hence  if  the  a  particles  are  helium  atoms  they  must  carry 
a  double  charge ;  the  large  value  of  e/m  shows  that  the 
carriers  of  the  positive  charge  must  be  atoms,  or  molecules 
of  some  substance  with  a  small  atomic  weight.  Hydrogen 
and  helium  are  the  only  substances  with  an  atomic  weight 
small  enough  to  be  compatible  with  so  large  a  value  of  e/m 
as  5,000,  and  of  these,  helium  is  known  to  be  given  off 
by  radio-active  substances,  whereas  we  have  as  yet  no 
evidence  that  there  is  any  evolution  of  hydrogen. 

Positive  particles  having  e/m  —  5  X  103  are  found, 
as,  we  have  seen,  in  all  vacuum  tubes  carrying  an  electric 
discharge  when  the  pressure  in  the  tube  is  very  low ; 
the  velocity  of  these  particles  is  very  much  less  than 
that  of  the  a  particles.  From  the  researches  of 
Bragg,  Kleeman,  and  Rutherford,  it  appears  that  the  a 
particles  lose  their  power  of  ionisation  and  of  producing 
phosphorescence  when  their  velocity  is  reduced  by  passing 
through  absorbing  substances  to  about  109  em/sec.  The 


COKPUSCLES  IN  VACUUM  TUBES.     25 

interesting  point  about  this  result  is  that  the  positively 
electrified  particles  in  a  discharge  tube  can  produce  ionisa- 
tion  and  phosphorescence  when  their  velocity  is  very  much 
smaller  than  this. 

This  may  possibly  be  due  to  the  a  particles  being  much 
fewer  in  number  than  the  positively  charged  particles  in  a 
discharge  tube  ;  and  that  as  the  a  particles  are  so  few  and 
far  between,  a  particle  in  its  attempts  at  ionisation  or  at 
producing  phosphorescence  receives  no  assistance  from  its 
companions.  Thus,  if  ionisation  or  phosphorescence  requires 
a  certain  amount  of  energy  to  be  communicated  to  a 
system,  all  that  energy  has  to  come  from  one  particle. 
When,  however,  as  in  a  discharge  tube,  the  stream  of 
particles  is  much  more  concentrated,  the  energy  required 
by  the  system  may  be  derived  from  more  than  one  particle, 
the  energy  given  to  the  system  by  one  particle  not  having 
been  entirely  lost  before  additional  energy  is  supplied  by 
another  particle.  Thus  the  effects  produced  by  the  particles 
might  be  cumulative  and  the  system  might  ultimately 
receive  the  required  amount  of  energy  by  contributions  from 
several  particles.  Thus,  although  the  contribution  from 
any  one  particle  might  be  insufficient  to  produce  ionisation 
or  phosphorescence,  the  cumulative  effects  of  several  might 
be  able  to  do  so. 

Another  way  in  which  the  sudden  loss  of  ionising  power 
might  occur  is  that  the  power  of  producing  ionisation  may 
be  dependent  on  the  possession  of  an  electric  charge  by 
the  particle,  and  that  when  the  velocity  of  the  particle 
falls  below  a  certain  value,  the  particle  is  no  longer  able  to 
escape  from  a  negatively  charged  corpuscle  when  it  passes 
close  to  it,  but  retains  the  corpuscle  as  a  kind  of  satellite, 
the  two  forming  an  electrically  neutral  system,  and  that 
inasmuch  as  the  chance  of  ionisation  by  collision  diminishes 
as  the  velocity  increases,  when  the  velocity  exceeds  a  certain 
value,  such  a  neutral  system  is  not  so  likely  to  be  ionised 
and  again  acquire  a  charge  of  electricity  as  the  more  slowly 
moving  particles  in  a  discharge  tube. 

These  investigations  on  the  properties  of  the  carriers  of 


26  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

positive  electricity  prove :  (1)  that  whereas  in  gases  at  very 
low  pressures  the  carriers  of  negative  electricity  have  an  ex- 
ceedingly small  mass,  only  about  1/1700  of  that  of  the 
hydrogen  atom,  the  mass  of  the  carriers  of  positive  elec- 
tricity is  never  less  than  that  of  the  hydrogen  atom ; 
(2)  that  while  the  carrier  of  negative  electricity,  the  cor- 
puscle, has  the  same  mass  from  whatever  source  it  may  be 
derived,  the  mass  of  the  carrier  of  the  positive  charge  may 
be  variable :  thus  in  hydrogen  the  smallest  of  the  positive 
particles  seems  to  be  the  hydrogen  atom,  while  in  helium, 
at  not  too  low  a  pressure,  the  carrier  of  the  positive  electricity 
is  partly,  at  any  rate,  the  helium  atom.  All  the  evidence 
at  our  disposal  shows  that  even  in  gases  at  the  lowest  pres- 
sures the  positive  electricity  is  always  carried  by  bodies  at 
least  as  large  as  atoms ;  the  negative  electricity,  on  the  other 
hand,  is  under  the  same  circumstances  carried  by  corpuscles, 
bodies  with  a  constant  and  exceedingly  small  mass. 

The  simplest  interpretation  of  these  results  is  that  the 
positive  ions  are  the  atoms  or  groups  of  atoms  of  various 
elements  from  which  one  or  more  corpuscles  have  been 
removed.  That,  in  fact,  the  corpuscles  are  the  vehicles  by 
which  electricity  is  carried  from  one  body  to  another,  a 
positively  electrified  body  differing  from  the  same  body 
when  unelectrified  in  having  lost  some  of  its  corpuscles  while 
the  negative  electrified  body  is  one  with  more  corpuscles 
than  the  unelectrified  one. 

In  the  old  one-fluid  theory  of  electricity,  positive  or 
negative  electrification  was  due  to  an  excess  or  deficiency 
of  an  "  electric  fluid."  On  the  view  we  are  considering 
positive  or  negative  electrification  is  due  to  a  defect  or 
excess  in  the  number  of  corpuscles.  The  two  views  have 
much  in  common  if  we  suppose  that  the  "  electric  fluid  " 
is  built  up  of  corpuscles. 

In  the  corpuscular  theory  of  matter  we  suppose  that  the 
atoms  of  the  elements  are  made  up  of  positive  and  negative 
electricity,  the  negative  electricity  occurring  in  the  form  of 
corpuscles.  In  an  unelectrified  atom  there  are  as  many  units 
of  positive  electricity  as  there  are  of  negative  ;  an  atom  with 


COEPUSCLES  IN  VACUUM  TUBES.     27 

a  unit  positive  charge  is  a  neutral  atom  which  has  lost  one 
corpuscle,  while  an  atom  with  a  unit  negative  charge  is  a 
neutral  atom  to  which  an  additional  corpuscle  has  been 
attached.  No  positively  electrified  body  has  yet  been  found 
with  a  mass  less  than  that  of  a  hydrogen  atom.  We  cannot, 
however,  without  further  investigation  infer  from  this  that 
the  mass  of  the  unit  charge  of  positive  electricity  is  equal 
to  the  mass  of  the  hydrogen  atom,  for  all  we  know  about  the 
electrified  system  is,  that  the  positive  electricity  is  in  excess 
by  one  unit  over  the  negative  electricity ;  any  system  con- 
taining n  units  of  positive  electricity  and  (n  - 1)  corpuscles 
would  satisfy  this  condition  whatever  might  be  the  value 
of  11.  Before  we  can  deduce  any  conclusions  as  to  the  mass 
of  the  unit  of  positive  electricity  we  must  know  something 
about  the  number  of  corpuscles  in  the  system.  We  shall 
give,  later  on,  methods  by  which  we  can  obtain  this  infor- 
mation ;  we  may,  however,  state  here  that  these  methods 
indicate  that  the  number  of  corpuscles  in  an  atom  of  any 
element  is  proportional  to  the  atomic  weight  of  the  element 
— it  is  a  multiple,  and  not  a  large  one,  of  the  atomic  weight  of 
the  element.  If  this  result  is  right,  there  cannot  be  a  large 
number  of  corpuscles  and  therefore  of  units  of  positive 
electricity  in  an  atom  of  hydrogen,  and  as  the  mass  of  a 
corpuscle  is  very  small  compared  with  that  of  an  atom  of 
hydrogen,  it  follows  that  only  a  small  fraction  of  the  mass 
of  the  atom  can  be  due  to  the  corpuscle.  The  bulk  of  the 
mass  must  be  due  to  the  positive  electricity,  and  therefore 
the  mass  of  unit  positive  charge  must  be  large  compared 
with  that  of  the  corpuscle — the  unit  negative  charge. 

From  the  experiments  described  on  p.  19  we  conclude 
that  positive  electricity  is  made  up  of  units,  which  are  inde- 
pendent of  the  nature  of  the  substance  which  is  the  seat  of 
the  electrification. 


CHAPTEE    II. 

THE    ORIGIN    OF    THE    MASS    OF    THE    CORPUSCLE. 

THE  origin  of  the  mass  of  the  corpuscle  is  very  interesting, 
for  it  has  been  shown  that  this  mass  arises  entirely  from 
the  charge  of  electricity  on  the  corpuscle.  We  can  see 
how  this  comes  about  in  the  following  way.  If  I  take 
an  uncharged  body  of  mass  M  at  rest  and  set  it  moving 
with  the  velocity  V,  the  work  I  shall  have  to  do  on 
the  body  is  equal  to  the  kinetic  energy  it  has  acquired, 
i.e.,  to  J  MV2.  If,  however,  the  body  is  charged  with 
electricity  I  shall  have  to  do  more  work  to  set  it  moving 
with  the  same  velocity,  for  a  moving  charged  body  pro- 
duces magnetic  force,  it  is  surrounded  by  a  magnetic  field 


FIG.    12. 

and  this  field  contains  energy;  thus  when  I  set  the  body 
in  motion  I  have  to  supply  the  energy  for  this  magnetic  as 
well  as  for  the  kinetic  energy  of  the  body.  If  the  charged 
body  is  moving  along  the  line  OX,  the  magnetic  force  at  a 
point  P  is  at  right  angles  to  the  plane  POX ;  thus  the  lines 
of  magnetic  forces  are  circles  having  OX  for  their  axis.  The 

magnitude  of  the  force  at  P  is  equal  to  e  V  s™'  6  where  6 

denotes  the  angle  POX.  Now  in  a  magnetic  field  the  energy 
per  unit  volume  at  any  place  where  the  magnetic  force  is 


ORIGIN   OF   THE   MASS   OF   THE   CORPUSCLE.  29 

equal  to  H  is  H'2/S-n:  Thus  the  energy  per  unit  volume  at 
P  arising  from  the  magnetic  force  produced  by  the  moving 

"I         ?2  T/2  QJ'II  2  /) 

charge  is   —  -  — ,  and  by  taking   the   sum  of   the 

OTT  C/x 

energy  throughout  the  volume  surrounding  the  charge,  we 
find  the  amount  of  energy  in  the  magnetic  field.  If  the 
moving  body  is  a  conducting  sphere  of  radius  a,  a  simple 
calculation  shows  that  the  energy  in  the  magnetic  field  is 

equal  to  ~         — .     The  energy  which  has  to  be  supplied  to 
o        ci 

set  the  sphere  in  motion  is  this  energy  plus  the  kinetic 
energy  of  the  sphere,  i.e.,  it  is  equal  to 

-  m  F2  +  l  ~  V- 
2  r  3  a 

'    i(-+i£ 

Thus  the   energy  is  the  same   as  if   it  were  the  kinetic 

2  e2 

energy  of  a  sphere  with  a  mass  m  +  «  — instead  of  m. 

o    a 

Thus  the  apparent  mass  of  the  electrified  body  is  not  m  but 

m  -j-  _   —.     The  seat  of  this  increase  in  mass  is  not  in  the 
3     a 

electrified  body  itself  but  in  the  space  around  it,  just  as  if 
the  ether  in  that  space  were  set  in  motion  by  the  passage 
through  it  of  the  lines  of  force  proceeding  from  the  charged 
body,  and  that  the  increase  in  the  mass  of  the  charged 
body  arose  from  the  mass  of  the  ether  set  in  motion  by  the 
lines  of  electric  force.  It  may  make  the  consideration  of 
this  increase  in  mass  clearer  if  we  take  a  case  which  is  not 
electrical  but  in  which  an  increase  in  the  apparent  mass 
occurs  from  causes  which  are  easily  understood.  Suppose 
that  we  start  a  sphere  of  mass  M  with  a  velocity  V  in  a 
vacuum,  the  work  which  has  to  be  done  on  the  sphere  is 
\  M  F2.  Let  us  now  immerse  the  sphere  in  water  :  the 
work  required  to  start  the  sphere  with  the  same  velocity 
will  evidently  be  greater  than  when  it  was  in  the  vacuum,  for 
the  motion  of  the  sphere  will  set  the  water  around  it  in 


30  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

motion.  The  water  will  have  kinetic  energy,  and  this,  as 
well  as  the  kinetic  energy  of  the  sphere,  has  to  be  supplied 
when  the  sphere  is  moved.  It  has  been  shown  by  Sir 
George  Stokes  that  the  energy  in  the  water  is  equal  to 
\  MI  F2  where  MI  is  the  mass  of  half  the  volume  of  the 
water  displaced  by  the  sphere.  Thus  the  energy  required 
to  start  the  sphere  is  J  (M  +  MI)  F2,  and  the  sphere 
behaves  as  if  its  mass  were  M  +  MI  and  not  M,  and  for 
many  purposes  we  could  neglect  the  effect  of  the  water  if 
we  supposed  the  mass  of  the  sphere  to  be  increased  in  the 
way  indicated.  If  we  suppose  the  lines  of  electric  force 
proceeding  from  the  charged  body  to  set  the  ether  in 
motion  and  assume  the  ether  has  mass,  then  the  origin  of  the 
increase  of  mass  arising  from  electrification  would  be  very 
analogous  to  the  case  just  considered.  The  increase  in 

2    ft 

mass  due  to  the  charge  is  -     -  ;  thus  for  a  given  charge 

8     a 

the  increase  in  the  mass  is  greater  for  a  small  body  than  for 
a  large  one.  Now  for  bodies  of  ordinary  size  this  increase 
of  mass  due  to  electrification  is  for  any  realisable  charges 
quite  insignificant  in  comparison  with  the  ordinary  mass. 
But  since  this  addition  to  the  mass  increases  rapidly  as 
the  body  gets  smaller,  the  question  arises,  whether  in  the 
case  of  these  charged  and  exceedingly  small  corpuscles 
the  electrical  mass,  as  we  may  call  it,  may  not  be  quite 
appreciable  in  comparison  with  the  other  (mechanical)  mass. 
We  shall  now  show  that  this  is  the  case;  indeed  for 
corpuscles  there  is  no  other  mass :  all  the  mass  is 
electrical. 

The  method  by  which  this  result  has  been  arrived  at  is 
as  follows:  The  distribution  of  magnetic  force  near  a 
moving  electrified  particle  depends  upon  the  velocity  of 
the  particle,  and  when  the  velocity  approaches  that  of  light, 
is  of  quite  a  different  character  from  that  near  a  slowly 
moving  particle.  Perhaps  the  clearest  way  of  seeing  this  is 
to  follow  the  changes  which  occur  in  the  distribution  of  the 
electric  force  round  a  charged  body  as  its  velocity  is 
gradually  increased.  When  the  body  is  at  rest  the  electric 


OEIGIN   OF   THE   MASS   OF    THE   CORPUSCLE.    31 

force  is  uniformly  distributed  round  the  body,  i.e.,  as  long 
as  we  keep  at  the  same  distance  from  the  charged  body 
the  electric  force  remains  the  same  whether  we  are  to  the 
east,  west,  north  or  south  of  the  particle  ;  the  lines  of  force 
which  come  from  the  body  spread  out  .uniformly  in  all 
directions.  When  the  body  is  moving  this  is  no  longer  the 
case,  for  if  the  body  is  moving  along  the  line  OA  (Fig.  13), 
the  lines  of  electric  force  tend  to  leave  the  regions  in  the 
neighbourhood  of  OA  and  OB,  which  we  shall  call  the 
polar  regions,  and  crowd  towards  a  plane  drawn  through 
O  at  right  angles  to  OA  ;  the  regions  in  the  neighbourhood 


FIG.    13 

of  this  plane  we  shall  call  the  equatorial  regions.  This 
crowding  of  the  lines  of  force  is  exceedingly  slight  when  the 
velocity  of  the  body  is  only  a  small  fraction  of  that  of  light, 
but  it  becomes  very  marked  when  the  velocity  of  the  body 
is  nearly  equal  to  that  velocity  ;  and  when  the  body  moves 
at  the  same  speed  as  light  all  the  lines  of  force  leave  the 
region  round  OA  and  crowd  into  the  plane  through  0  at 
right  angles  to  OA,  i.e.,  the  lines  of  force  have  swung  round 
until  they  are  all  at  right  angles  to  the  direction  in  which 
the  particle  is  moving.  The  effect  of  this  crowding  of  the 
lines  of  force  towards  the  equatorial  plane  is  to  weaken  the 
magnetic  force  in  the  polar  and  increase  it  in  the  equatorial 


32  THE  CORPUSCULAR  THEOEY  OF  MATTEE. 

regions.  The  polar  regions  are  those  where  the  magnetic 
force  was  originally  weak,  the  equatorial  regions  those 
where  it  was  strong.  Thus  the  effect  of  the  crowding  is 
to  increase  relatively  the  strength  of  the  field  in  the  strong 
parts  of  the  field  and  to  weaken  it  in  the  weak  parts.  This 
makes  the  energy  in  the  field  greater  than  if  there  were  no 

crowding,  in  which  case  the  energy  is  —   — —where  e  is 

o       a 

the  charge,  v  the  velocity  and  a  the  radius  of  the  sphere. 
When  we  allow7  for  the  crowding,  the  energy  will  be 

a         — ,  where  a  is  a  quantity  which  will  be  equal  to 
o  a 

unity  when  v  is  small  compared  with  c  the  velocity  of 
light,  but  becomes  very  large  when  v  approaches  c.  The 

O  2 

part  of  the  mass  arising  from  the  charge  is  —  «  —  t    thus 

O  Cl 

since  a  depends  npon  r  —  the  velocity  of  the  particle  —  the 
electrical  mass  will  depend  upon  v,  and  thus  this  part  of 
the  mass  has  the  peculiarity  that  it  is  not  constant  but 
depends  upon  the  velocity   of   the    particle.      Thus  if  an 
appreciable  part  of  the  mass  of  the  corpuscle  is  electrical 
in  origin,  the  mass  of  rapidly  moving  corpuscles  will  be 
greater  than  that  of  slow  ones,  while  if  the  mass  were  in 
the  main  mechanical,    it    would    be    independent    of    the 
velocity.     Eadium  gives  out  corpuscles  which  move  with 
velocities  comparable  with  that   of   light   and   which   are 
therefore  very   suitable   for  testing  whether    or   not   this 
increase  in  the  mass  of  a  corpuscle  with  its  velocity  takes 
place.     This  test  has  been  applied  by  Kaufmann,  who  has 
measured  the  value  of  m/e  for  the  various  corpuscles  moving 
with  different  velocities  given  out  by  radium.      We   can 
calculate  the  value  of  the  coefficient  a— the  quantity  which 
expresses  the  effect  of  the  velocity  on  the  mass.     The  value 
of  this  quantity  depends  to  some  extent  on  the  view  we 
take  as  to  the  distribution  of  electricity  on  the  corpuscle ; 
we  get  slightly  different  values  according  as  we  suppose 
the  electricity  to  be  distributed  over  the  surface  of  a  con- 
ducting sphere  of  radius  a,  or  rigidly  distributed  over  the 


OBIGIN    OF   THE    MASS   OF   THE    COEPUSCLE.  33 


surface  of  a  non-conducting  sphere  of  the  same  radius,  or 
uniformly  distributed  throughout  the  volume  of  such  a 
sphere.  In  calculating  these  differences  we  have  to  suppose 
the  charge  on  the  sphere  divided  up  into  smaller  parts  and 
that  each  of  these  small  parts  obeys  the  ordinary  laws  of 
electrostatics.  If  we  suppose  that  the  charge  on  the 
corpuscles  is  the  unit  of  negative  electricity,  it  is  not 
permissible  to  assume  that  smaller  portions  will  obey  the 
ordinary  laws  of  electrostatic  attraction. 

Perhaps  the  simplest  assumption  we  can  make  is  that 
the  energy  is  the  same  as  that  outside  a  sphere  of  radius  a 
moving  with  the  velocity  V  and  with  a  charge  e  at  its 
centre.  I  have  calculated  the  value  of  a  on  this  supposition ; 
the  results  are  given  in  the  following  Table.  The  first 
column  of  the  Table  contains  the  velocity  of  the  corpuscles, 
which  were  the  object  of  Kaufmann's  experiments ;  the 
second  column,  the  values  found  by  Kaufmann  for  the  ratio 
of  the  mass  of  corpuscles  moving  with  this  velocity  to 
the  mass  of  a  slowly  moving  corpuscle,  and  the  third 
column  the  value  of  a  calculated  on  the  preceding 
hypothesis. 


Velocity  of  Corpuscle. 

Katio  of  Mass  to  that  of  a  Slow 
Corpuscle. 

a 

2-85  X  1010  cm/sec. 

3-09 

3-1 

2'72  X  1010  cm/sec. 

2-43 

2-42 

2-59  X  1010  cm/sec. 

2-04 

2-0 

2'48  X  1010  cm/sec. 

1-83 

1-66 

2-36  X  1010  cm/sec. 

1-65 

1-5 

You  will  notice  that  the  second  and  third  columns  are 
almost  identical ;  the  second  column,  however,  expresses 
the  increase  of  the  whole  mass ;  the  third  column,  the 
increase  of  the  electrical  mass.  We  see  that  these  are 
practically  equal  to  each  other,  hence  we  conclude  that  the 
whole  of  the  mass  of  the  corpuscle  is  electrical.  This  elec- 
trical mass  has  its  origin  in  the  region  round  the  corpuscle 

T.M.  D 


84  THE  COKPUSCULAK  THEOKY  OF  MATTEE. 

and  is  not  resident  in  the  corpuscle  itself ;  hence,  from  our 
point  of  view,  each  corpuscle  may  be  said  to  extend  through- 
out the  whole  universe,  a  result  which  is  interesting  in 
connection  with  the  dogma  that  two  bodies  cannot  occupy 
the  same  space. 

From  the  result  that  the  whole  of  !he  mass  is  electrical 
we  are  able  to  deduce  the  size  of  the  corpuscle,  for  if  m 
is  the  mass, 

2  e* 
m  =  ~  — . 

3  a 

Now  we  have  seen  that  e/m  =  1*7  X  107,  and  that  in 
electromagnetic  measure  e  =  1020.  Substituting  these  values 
we  find  that  a  the  radius  of  the  corpuscle  —  10~13  cm.  The 
radius  of  the  atom  is  usually  taken  as  about  10~8  cm.,  hence 
the  radius  of  a  corpuscle  is  only  about  the  one-hundred- 
thousandth  part  of  the  radius  of  the  atom.  The  potential 

energy  due  to  the  charge  is  -  — ,  if  V  is  the  velocity  of 

2i      a 

light ;  this  potential  energy  is  about  the  same  in 
amount  as  the  kinetic  energy  possessed  by  an  a  particle 
moving  with  a  velocity  about  one-fiftieth  that  of  light. 

EVIDENCE  OF  THE  EXISTENCE  OF  COKPUSCLES  AFFORDED  BY 
THE  ZEEMAN  EFFECT. 

The  existence  of  corpuscles  is  confirmed  in  a  very 
striking  way  by  the  effect  produced  by  a  magnetic  field 
on  the  lines  of  the  spectrum  and  known  as  the  Zeeman 
effect.  Zeeman  found  that  when  the  luminous  body 
giving  out  the  spectrum  is  placed  in  a  strong  magnetic 
field,  many  of  the  lines  which  are  single  before  the 
application  of  the  field  are  resolved  into  three  or  more 
components.  The  simplest  case  is  when  a  line  originally 
single  is  resolved  into  three  components,  the  luminous  body 
being  looked  at  in  a  direction  at  right  angles  to  the  lines  of 
magnetic  force ;  the  middle  line  of  the  three  occupies  its 
old  position,  and  the  side  lines  are  separated  from  it  by  an 
amount  proportional  to  the  magnetic  force.  All  the  lines 


OKIGIN   OF   THE   MASS   OF   THE    COKPUSCLE.   35 

are  plane  polarised,  the  plane  of  polarisation  of  the  middle 
line  being  at  right  angles  to  that  of  the  side  lines.  If  the 
same  line  is  looked  at  in  the  direction  of  the  magnetic  force, 
the  middle  line  is  absent  and  the  two  side  lines  are 
circularly  polarised  in  opposite  senses. 

The  theory  of  this  simple  case,  which  was  first  given  by 
Lorentz,  is  as  follows :  Let  us  assume  that  the  vibrating 
system  giving  out  the  line  is  a  charged  body,  and  that  it  is 
vibrating  under  the  action  of  a  force  whose  magnitude  is 
directly  proportional  to  the  distance  of  the  vibrating  body 
from  a  fixed  point,  and  whose  direction  always  passes 
through  the  point.  Suppose  that  O  is  the  fixed  point  and 
P  the  electrified  body,  and  let  us  suppose  that  the  latter  is 
describing  a  circular  orbit  round  0 ;  let  m  be  the  mass  of 


FIG.  14. 


the  body,  f<OP  the  force  acting  upon  it  ;  then  the  radial 
acceleration  towards    0   is   equal   to   v2/OP,   v   being  the 
velocity  of  the  body.    But  the  product  of  the  mass  and  the 
radial  acceleration  is  equal  to  the  radial  force  pOP,  hence 
m  v2 


OP 

If  w  is  the  angular  velocity,  v  =  w.OP,  hence 

f-JLn     w=      /Z 

m  V  m 

The  time  of  vibration  is  the  time  OP  takes  to  make  a 
complete  revolution  or  STT/W  ;  thus  w,  which  is  called  the 
frequency  of  the  vibration,  is  proportional  to  the  number  of 
vibrations  per  second.  In  this  case  the  frequency  of  vibra- 
tion will  evidently  be  the  same  whether  P  goes  round  0  in 
the  direction  of  the  hands  of  a  watch  or  in  the  opposite 

D2 


36     THE  CORPUSCULAK    THEORY   OF   MATTER. 

direction.  Let  now  a  magnetic  force  at  right  angles  to  the 
plane  of  the  paper  and  downwards  act  upon  the  charged 
body.  As  we  have  had  occasion  to  remark  before,  when  a 
charged  body  moves  in  a  magnetic  field  it  is  acted  upon  by 
a  force  which  is  at  right  angles  to  its  direction  of  motion 
and  also  to  the  magnetic  force,  and  equal  to  Hev  sin  0 
where  H  is  the  magnetic  force,  e  the  charge  on  the  body,  v 
its  velocity,  and  0  the  angle  between  the  directions  of  H 
and  v. 

Let  now  the  charged  particle  be  describing  a  circle  in  the 
direction  indicated  by  the  arrow  round  0,  the  magnetic 
force  being  at  right  angles  to  the  plane  of  the  paper  and 
downwards.  The  force  due  to  the  magnetic  field  will  be  radial 
and  in  this  case  directed  inwards,  and  equal  to  Hev,  hence, 
in  addition  to  the  radial  force  /x.OP,  we  have  the  force 
Hev  ;  equating  the  product  of  the  mass  and  the  radial 
acceleration  to  the  radial  force  we  have 


He'  v 

and  since  v  =  w  X  OP 


m          m  2     m          v   m        4m 

thus  w  is  greater  than  before,  and  if  /*/m  is  large  compared 
with  He/m  and  equal  to  w20  we  have 

1  He 

W  =  "*  +  2  ^ 
approximately  ;    w0  is  the  frequency  without  the  magnetic 

field,  thus  the  change  in   the  frequency  is  --  —  -,   and   in 

2     m 

this  case  it  is  an  increase. 

Suppose,  however,  that  P  were  describing  the  circle 
in  the  opposite  direction,  then,  since  the  direction  of 
motion  is  reversed  the  force  produced  by  the  magnetic 
field  will  be  reversed  and  the  force  will  now  be  outwards 
instead  of  inwards  ;  thus,  instead  of  equation  (1)  we  have 

m  V2 

—  := 


ORIGIN   OF    THE  MASS   OF   THE    CORPUSCLE.    37 

and  this  treated  in  the  same  way  as  equation  (1)  leads  to 
the  result 

1  He 

w   =   w 

2  m 

Thus  the  frequency  of  vibrations  in  this  direction  is 
diminished  by  an  amount  equal  to  that  by  which  the 
frequency  in  the  opposite  direction  is  increased.  Thus  the 
charged  body  will  go  round  faster  in  one  direction  than 


FIG.  15. 


in  the  opposite.  I  have  here  an  experiment  to  illustrate  a 
similar  effect  in  a  mechanical  system.  A  conical  pendulum 
has  for  the  bob  a  fly  wheel  which  can  be  caused  to  rotate  about 
its  axis  of  rotation.  The  rotating  fly  wheel  causes  a  force 
to  act  on  the  bob  of  the  pendulum ;  this  force  is  at  right 
angles  to  the  direction  of  motion  of  the  bob,  and  is 
proportional  to  its  velocity.  It  is  thus  analogous  to 
the  force  acting  on  the  charged  particle  due  to  the 
magnetic  field.  The  radial  force  on  the  electrified  particle 


38  THE  COKPUSCULAK  THEOEY  OF  MATTEE. 

is  represented  by  the  component  of  gravity  at  right  angles 
to  the  axis  of  the  pendulum.  I  set  this  pendulum  swinging 
as  a  conical  pendulum  with  the  fly  wheel  not  in  rotation. 
As  you  would  naturally  suppose,  it  goes  round  just  as  fast  in 
the  direction  of  the  hands  of  a  watch  as  in  the  opposite 
direction.  I  now  set  the  fly  wheel  in  rapid  rotation  and 
repeat  the  experiment.  You  see  that  now  the  pendulum 
goes  round  distinctly  more  rapidly  in  one  direction  than  in 
the  opposite,  and  the  direction  in  which  the  rotation  is  most 
rapid  is  that  in  which  the  rotation  of  the  pendulum  is  in  the 
same  direction  as  that  of  the  fly  wheel. 

We  see  from  these  considerations  that  a  corpuscle  which, 
when  free  from  magnetic  force,  would  vibrate  with  the  same 
frequency  in  whatever  direction  it  might  be  displaced  will 
no  longer  do  so  when  placed  in  a  magnetic  field.  If  the 
corpuscle  is  displaced  so  as  to  move  along  the  lines  of 
magnetic  force,  the  force  on  the  corpuscle  due  to  the 
magnetic  field  will  vanish,  since  it  is  proportional  to 
the  sine  of  the  angle  between  the  magnetic  force  and  the 
direction  of  motion  of  the  particle  ;  and  in  this  case  the 
frequency  will  be  the  same  as  without  the  field.  When, 
however,  the  corpuscle  vibrates  in  the  plane  at  right  angles 
to  the  lines  of  magnetic  force  the  frequency  will  be  w  + 

J  -   -  if  it  goes  round  in  one  direction,  and  w  —  J  -  -  il 

it  goes  round  in  the  other.  Thus  in  the  magnetic  field 
the  corpuscles  will  vibrate  with  the  three  frequencies  w, 

o>  +  ^  — ,  o)  —  i  — - ;    one  of    these    being   the  same  as 
"   m  m 

when  it  was  undisturbed.  Thus,  in  the  spectroscope 
there  will  be  three  lines  instead  of  one,  the  middle  line 
being  in  the  undisturbed  position.  If,  however,  we  look  at 
the  corpuscle  in  the  direction  of  the  magnetic  force,  since 
the  vibrations  corresponding  to  the  undisturbed  position  of 
the  lines  are  those  in  which  the  vibrations  are  along  the 
lines  of  magnetic  force,  and  since  a  vibrating  electrified 
particle  does  not  send  out  any  light  along  the  line  of  its 
vibration,  no  light  will  come  from  the  corpuscle  to  an  eye 


ORIGIN   OF   THE   MASS   OF   THE    CORPUSCLE.   39 

situated  along  a  line  of  magnetic  force  passing  through  the 
corpuscle,  so  that  in  this  case  the  central  line  will  be  absent, 
while  the  two  side  lines  which  correspond  to  circular  orbits 
described  by  the  corpuscle  in  opposite  directions  will  give 
rise  to  circularly  polarised  light.  By  finding  the  sense  of 
rotation  of  the  light  in  the  line  whose  frequency  is  greater 
than  the  undisturbed  light,  it  has  been  shown  that  the 
light  is  due  to  a  negatively  electrified  body.  By  measuring 
the  displacement  of  the  lines  we  can  determine  the  change 

in  frequency,  i.e.,  J  -— ,  so  that  if  H  is  known,  e/m  can  be 

determined.  In  this  way  Zeeman  has  found  the  value  of 
e/m  to  be  of  the  order  107,  the  same  as  that  deduced  by  the 
direct  methods  previously  described.  The  values  of  e/m 
got  in  this  way  are  not  the  same  for  all  lines  of  the  spectra, 
but  when  the  lines  are  divided  up  into  series,  as  in  Paschen 
and  Runge's  method,  the  different  lines  in  the  same  series 
all  give  the  same  value  of  ejm. 

The  displacement  of  the  lines  produced  by  the  magnetic 
field  is  proportional  to  e/m,  and  thus  for  light  due  to  the 
oscillations  of  a  corpuscle  the  displacement  will  be  more 
than  a  thousand  times  greater  than  that  due  to  the  vibra- 
tion of  any  positive  ion  with  which  we  are  acquainted.  It 
requires  very  delicate  apparatus  to  detect  the  displacement 
when  e/m  is  10r :  a  displacement  one-thousandth  part  of 
this  would  be  quite  inappreciable  by  any  means  at  present 
at  our  disposal,  hence  we  may  conclude  that  the  light  in 
any  lines  which  show  the  Zeeman  effect  (and  in  line 
spectra  as  distinct  from  band  spectra,  all  lines  do  show  this 
effect  to  some  extent)  is  due  to  the  vibrations  of  corpuscles 
and  not  of  atoms. 

The  Zeeman  effect  is  so  important  a  method  of  finding 
out  something  about  the  structure  of  the  atom  and  the 
nature  of  the  vibrating  systems  in  a  luminous  gas,  that  it 
is  desirable  to  consider  a  little  more  in  detail  the  nature  of 
the  conclusions  to  be  drawn  from  this  effect.  In  the  first 
place  it  is  only  a  special  type  of  vibration  that  will  show 
the  Zeeman  effect.  The  simple  case  we  considered  was 


40  THE  CORPUSCULAR  THEOEY  OF  MATTEK. 

when  the  corpuscle  was  attracted  to  O  (Fig.  14)  by  a  force 
proportional  to  OP;  this  force  is  the  same  in  all  directions, 
so  that  if  the  corpuscle  is  displaced  from  0  and  then  let  go  it 
will  vibrate  in  the  same  period  in  whatever  direction  it  may 
be  displaced :  such  a  corpuscle  shows  the  Zeeman  effect. 
If,  however,  the  force  on  P  were  different  in  different 
directions  so  that  the  times  of  vibration  of  the  corpuscle 
depended  on  the  direction  in  which  it  was  displaced, 
then  the  vibrations  would  not  have  shown  this  effect. 
The  influence  of  the  magnetic  force  would  have  been  of  a 
lower  order  altogether  than  in  the  preceding  case.  A  single 
particle  placed  in  a  field  of  force  of  the  most  general 
character  might  vibrate  with  three  different  periods  and 
thus  give  out  a  spectrum  containing  three  lines,  but  if  such 
a  particle  were  placed  in  a  magnetic  field  these  lines  would 
not  show  the  Zeeman  effect;  all  that  the  magnetic  force 


o o o 

FIG.   16. 

could  do  would  be  to  slightly  alter  the  periods  by  an  amount 
infinitesimal  in  comparison  with  that  observed  in  the 
Zeeman  effect.  There  could  be  no  resolution  of  the  lines 
into  triplets ;  it  is  only  in  the  special  case  when  the  periods 
all  become  the  same  that  the  Zeeman  effect  occurs.  We  can 
easily  imagine  cases  in  which  some  lines  might  show  the 
Zeeman  effect,  while  others  would  not  do  so.  Take  the  case 
of  two  corpuscles  A  and  B  attracted  to  a  point  0  (Fig.  16) 
and  repelling  each  other,  they  will  settle  into  a  position  of 
equilibrium  when  the  repulsion  between  them  balances  the 
attraction  exerted  by  0.  In  the  most  general  case  there 
would  be  six  different  frequencies  of  vibration  (each 
corpuscle  contributing  three)  and  none  of  these  would 
show  the  Zeeman  effect.  In  the  special  case  where  the 
force  exerted  by  0  is  the  same  in  all  directions,  three  of 
these  frequencies  coincide,  two  others  vanish,  and  there  is 
one  remaining  isolated.  The  spectrum  is  reduced  to  two 


OBIG1N   OF   THE   MASS   OF    THE    CORPUSCLE.   41 

lines  ;  one  of  these  (that  corresponding  to  the  coalescence 
of  the  three  lines)  would  show  the  normal  Zeeman  effect 
while  the  other  would  not  show  it  at  all.  With  more  com- 
plicated systems  we  might  have  several  lines  showing  the 
Zeeman  effect  accompanied  by  others  which  do  not  show  it. 
When  more  lines  than  one  show  the  Zeeman  effect,  the 
magnitude  of  the  effect  may  differ  from  line  to  line.  Thus, 
take  the  case  of  four  corpuscles  mutually  repelling  each 
other  and  attracted  towards  a  point  0.  In  the  most  general 
case  this  system  would  have  twelve  different  frequencies,  three 
for  each  corpuscle,  and  as  long  as  these  remained  different 
none  of  them  would  show  the  Zeeman  effect.  If,  however, 
the  force  exerted  by  0  is  the  same  in  all  directions,  two  sets 
of  three  of  these  frequencies  become  equal,  three  frequencies 
vanish,  two  others  coincide,  and  one  remains  isolated;  the 
twelve  frequencies  are  110 w  reduced  to  four,  the  two  lines  cor- 
responding to  the  sets  of  three  frequencies  which  had  coalesced 
will  both  show  the  Zeeman  effect,  but  not  to  the  same  extent, 
the  alteration  in  frequency  for  one  line  being  the  normal 

amount  \  — -  while  for  the  other  line  it  is  only  half  that 

Hi 

amount.  The  other  lines  do  not  show  the  Zeeman  effect. 
The  reader  who  is  interested  in  this  subject  is  referred  for 
other  instances  of  systems  illustrating  this  effect  to  a 
paper  by  the  writer  in  the  Proceedings  of  the  Cambridge 
Philosophical  Society,  vol.  xiii.,  p.  39. 

It  is  remarkable  that,  as  far  as  our  knowledge  extends,  all 
the  lines  in  a  line  spectrum  show  the  Zeeman  effect.  This 
might  arise  from  the  vibrating  systems  being  single 
corpuscles,  only  influenced  slightly,  if  at  all,  by  neigh- 
bouring corpuscles,  or  it  might  arise  from  the  vibrations  of 
more  complicated  systems,  provided  the  radiation  corre- 
sponding to  frequencies  which  on  the  theory  would  not  show 
the  Zeeman  effect,  has  great  difficulty  in  leaving  the 
vibrating  system.  We  have  an  example  of  the  second 
condition  in  the  case  of  two  corpuscles  shown  in  Fig.  16; 
the  vibration  which  does  not  show  the  Zeeman  effect  is  the 
one  when  the  middle  point  of  A  and  B  remains  at  rest 


42  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

and  A  and  B  are  approaching  0  or  receding  from  it  with 
equal  velocities ;  thus  the  charged  corpuscles  are  moving 
with  equal  velocities  in  opposite  directions  and  their  effects, 
at  a  distance  from  0  large  compared  with  OA  and  OB  will 
neutralise  each  other.  On  the  other  hand,  the  vibrations 
which  show  the  Zeeman  effect  are  those  in  which  A  and  B 
are  moving  in  the  same  direction,  so  that  the  effects  due  to 
one  will  supplement  those  due  to  the  other,  and  thus  the 
intensity  of  the  radiation  from  this  vibration  will  greatly 
exceed  that  from  the  other ;  thus  this  vibration  might  give 
rise  to  visible  radiation  while  the  other  did  not.  The 
vibration  of  a  system  of  corpuscles  which  produces  the 
greatest  effect  at  a  distance,  is  the  one  where  all  the 
corpuscles  move  with  the  same  speed  and  in  the  same 
direction  ;  it  can  be  easily  shown  that  for  this  case  the 
effect  of  a  magnetic  field  is  to  increase  or  dimmish  all  the 

frequencies  by  the  normal  amount  £ — -. 

"  in 

A  case  in  which  the  Zeeman  effect  might  be  abnormally 
large  is  the  following  : — Suppose  we  have  two  corpuscles 
A  and  B  moving  round  the  circumference  of  a  circle  with 
constant  angular  velocity  to,  always  keeping  at  opposite  ends 
of  a  diameter,  then  the  frequency  of  the  optical  or  magnetic 
effect  produced  by  this  system  is  not  co  but  2  o>,for  each  particle 
has  only  to  go  half  way  round  the  circumference  to  make  the 
state  of  the  system  recur.  If  now  we  place  the  system  in  a 
magnetic  field  where  the  magnetic  force  is  perpendicular  to 

the  circle  the  angular  velocity  o>  will  become  co  -f-  | —   and 

7/r 

the  frequency  of  the  system  2  w  -\-  — ,  thus  the  change  in 

the  frequency  is  — -,  which  is  twice  the  normal  effect. 
m 


CHAPTEE  III. 

PROPERTIES  OF  A  CORPUSCLE. 

HAVING  demonstrated  the  existence  of  corpuscles,  it  will 
be  convenient  for  purposes  of  reference  to  summarise  their 
properties. 

MAGNETIC  FORCE  DUE  TO  CORPUSCLES. 

A  moving  corpuscle  produces  around  it  a  magnetic  field. 
If  the  corpuscle  is  moving  in  a  straight  line  with  a  uniform 
velocity  v,  which  is  small  compared  with  the  velocity  of 


FIG.  17. 

light,  it  produces  a  magnetic  field  in  which  the  lines  of 
magnetic  force  are  circles  having  the  line  along  which 
the  corpuscle  is  moving  for  their  axis;  the  magni- 

tude of  the  force  at  a  point  P  is  equal  to  -2  sin  0,  where 


e  is  the  charge  on  the  moving  particle  0,  and  6  the 
angle  between  OP  and  OX  —  the  line  along  which  the 
corpuscle  is  moving.  The  direction  of  the  force  at  P 
(Fig.  17)  is  at  right  angles  to  the  plane  POX  and  down- 
wards from  the  plane  of  the  paper  if  the  negatively  charged 
particle  is  moving  in  the  direction  OX.  The  magnetic 
force  thus  vanishes  along  the  line  of  motion  of  the  particle 
and  is  greatest  in  the  plane  through  0  at  right  angles  to 


44  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

the  direction  of  motion  ;  the  distribution  of  force  is  sym- 
metrical with  respect  to  this  plane. 

If  the  velocity  of  the  uniformly  moving  particle  is  so 
great  that  it  is  comparable  with  c  the  velocity  of  light,  the 
intensity  of  the  magnetic  force  at  P  is  represented  by  the 
more  complicated  expression 


(' 
l" 


e  v  sin  6 


The  direction  of  the  force  is  the  same  as  before.  The  effect 
of  the  greater  velocity  is  to  make  the  magnetic  force 
relatively  weaker  in  the  parts  of  the  field  near  OX  and 
stronger  in  those  near  the  equatorial  plane,  until  when 
the  speed  of  the  corpuscle  is  equal  to  that  of  light  the 
magnetic  force  is  zero  everywhere  except  in  the  equatorial 
plane,  where  it  is  infinite. 

ELECTRIC  FIELD  ROUND  THE  MOVING  CORPUSCLE. 

The  direction  of  the  electric  force  at  P  is  along  OP,  and 
whatever  be  the  speed  at  which  the  corpuscle  is  moving, 
the  electric  force  E  and  the  magnetic  force  //  are  connected 
by  the  relation 

c2  H  =  v  E  sin  6  ; 

thus  when  the  corpuscle  is  moving  slowly 


the  same  value  as  when  the  particle  is  at  rest  (remembering 
that  e  is  measured  in  electro-magnetic  units). 
'  When  the  corpuscle  is  moving  more  rapidly  we  have 

2 


E  =  (c2  -  v2) 


r«  ( 1  —  ^0  sin 


(«•-? 


and  in  this  case  the  electric  force  is  no  longer  uniformly 
distributed,  but  is  more  intense  towards  the  equatorial 
regions  than  in  the  polar  regions  near  OX.  When  the 


PROPERTIES   OF   A   CORPUSCLE.  45 

corpuscle  moves  with  the  velocity  of  light  all  the  lines  of 
electric  force  are  in  the  plane  through  0  at  right  angles  to 
OX. 

When  the  corpuscle  is  moving  uniformly  the  lines  of  force 
are  carried  along  as  if  they 'were  rigidly  attached  to  it,  but 
when  the  velocity  of  the  corpuscle  changes  this  is  no  longer 
the  case,  and  some  very  interesting  phenomena  occur.  We 
can  illustrate  this  by  considering  what  happens  if  a  cor- 


FIG.  18. 

puscle  which  has  been  moving  uniformly  is  suddenly  stopped. 
Let  us  take  the  case  when  the  velocity  with  which  the  par- 
ticle is  moving  before  it  is  stopped  is  small  compared 
with  the  velocity  of  light;  then  before  the  stoppage  the 
lines  of  force  were  uniformly  distributed  and  were  moving 
forward  with  the  velocity  v.  When  the  corpuscle  is  stopped, 
the  ends  of  the  lines  of  force  on  the  corpuscle  will  be 
stopped  also ;  but  fixing  one  end  will  not  at  once  stop  the 
whole  of  the  line  of  force,  for  the  impulse  which  stops  the 
tube  travels  along  the  line  of  force  with  the  velocity  of 
light,  and  thus  takes  a  finite  time  to  reach  the  outlying 


46  THE  CORPUSCULAR  THEORY  OF  MATTER. 

parts  of  the  tube.  Hence  when  a  time  t  has  elapsed  after 
the  stoppage,  it  is  only  the  parts  of  the  lines  of  force 
which  are  inside  a  sphere  whose  radius  is  ct  which  have 
been  stopped.  The  lines  of  force  outside  this  sphere 
will  be  in  the  same  position  as  if  the  corpuscle  had 
not  been  stopped,  i.e.,  they  will  pass  through  0',  the 
position  the  corpuscle  would  have  occupied  at  the  time  t  if 
the  stoppage  had  not  taken  place.  Thus  the  line  of  force 
which,  when  the  corpuscle  was  stopped  was  in  the  position 
OQ  will,  at  the  time  t  be  distorted  in  the  way  shown  in 
Fig  18.  Inside  the  sphere  of  radius  ct  the  line  of  force  will 
be  at  rest  along  OQ  ;  outside  the  sphere  it  will  be  moving 
forward  with  the  velocity  v,  and  will  pass  through  0',  the 
point  O  would  have  reached  at  the  time  t  if  it  had  not  been 
stopped.  Since  the  line  of  force  remains  intact  it  must  be 
bent  round  at  the  surface  of  the  sphere  so  that  the  portion 
inside  the  sphere  may  be  in  connection  with  that  outside. 
Since  the  lines  of  force  along  the  surface  are  tangential 
there  will  be,  over  the  surface  of  the  sphere,  a  tangential 
electric  force.  This  tangential  force  will  be  on  the  surface 
of  a  sphere  of  radius  ct  and  will  travel  outwards  with  the 
velocity  of  light.  If  the  stoppage  of  the  sphere  took  a 
short  time  TT,  then  the  tangential  part  of  the  lines  of  force 
will  be  in  the  spherical  shell  between  the  spheres  whose 
radii  are  ct  and  c  (t  —  TT),  t  being  the  time  which  has  elapsed 
since  the  stoppage  began,  and  t  —  T  since  it  was  completed. 
This  shell  of  thickness  CTT,  filled  with  tangential  lines  of 
electric  force,  travels  outwards  with  the  velocity  of  light. 
The  electric  force  in  the  shell  is  very  large  compared  with  the 
force  in  the  same  region  before  the  shell  is  stopped.  We  can 
prove  that  the  magnitude  of  the  force  at  a  point  P  in  the  shell 

C    P    7?     S???    U 

is  equal  t        ,  where  S  is  the  thickness  of  the  shell, 

and  0  the  angle  POX.     Before  the  corpuscle  was  stopped 

o 

the  force  was  ,  thus  the  ratio  of  the  force  after  the 


stoppage  to  the  force  before  is  equal  to  V—~-  sin  0.      As  8 


PEOPEETIES   OF   A   COEPUSCLE.  47 

is  very  small  compared  with  OP,  this  ratio  is  very  large ; 
thus  the  stoppage  of  the  corpuscle  causes  a  thin  shell  of 
intense  electric  force  to  travel  outwards  with  the  velocity  of 
light.  These  pulses  of  intense  electric  force  constitute,  I 
think,  Eontgen  rays,  which  are  produced  when  cathode 
rays  are  suddenly  stopped  by  striking  against  a  solid 
obstacle.  The  electric  force  in  the  pulse  is  accompanied 

by  a  magnetic  force  equal  in  magnitude  to  ^^  —  and  at 

OP.  o 

right  angles  to  the  plane  POX.  The  energy  in  the  pulse 
due  to  this  distribution  of  magnetic  and  electric  force  is 

62      I-2 

equal   to  f  — — —  ;  it  is  thus  greater  when  the  thickness  of  the 

o 

pulse  is  small  than  when  it  is  large.  The  thickness  of  the 
pulse  is,  however,  proportional  to  the  abruptness  with 
which  the  corpuscle  is  stopped ;  and  as  the  energy  in  the 
pulse  is  radiated  away  it  follows  that  the  more  abruptly 
the  corpuscles  are  stopped  the  greater  the  amount  of  energy 
radiated  away  as  Eontgen  rays.  If  the  corpuscle  is  stopped 
so  abruptly  that  the  thickness  of  the  pulse  is  reduced  to 
the  diameter  of  the  corpuscle  the  whole  of  the  energy  in 
the  magnetic  field  round  the  corpuscle  is  radiated  away. 
If  the  corpuscle  is  stopped  more  slowly  only  a  fraction  of 
this  energy  escapes  as  Eontgen  rays. 

Inside  the  shell,  i.e.,  in  the  space  bounded  on  the  out- 
side by  the  sphere  of  radius  OP  (  =  ct),  there  is  no  mag- 
netic force,  while  outside  the  sphere  whose  radius  is  OP 
the  magnet  force  is  the  same  as  it  would  be  if  the  particle 
had  not  been  stopped,  i.e.,  at  the  point  Q  it  is  equal  to 

^77^2  sin  <£,  where  0'  is  where  0  would  have  been  if  the 
C/  (j/" 

corpuscle  had  gone  on  moving  uniformly,  and  <£  is  the  angle 
QO'  X.  The  pulse  in  its  outward  passage  wipes  out,  as 
it  were,  the  magnetic  force  from  each  place  as  it  passes 
over  it. 

We  have  seen  that  when  the  corpuscle  is  stopped  there 
is  a  pulse  of  strong  electric  and  magnetic  force  produced 
which  carries  energy  away.  It  is  not  necessary  that  the 


48  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

corpuscle  should  be  reduced  to  rest  for  this  pulse  to  be 
formed  ;  any  change  in  the  velocity  will  produce  a  similar 
pulse,  though  the  forces  in  the  pulse  will  not  be  so  intense 
as  when  the  stoppage  is  complete.  Since  any  change  in 
the  velocity  produces  this  tangential  electric  field,  such  a 
field  is  a  necessary  accompaniment  of  a  corpuscle  whose 
motion  is  accelerated,  and  we  can  show  that  if  when  at  0  the 
particle  has  an  acceleration/ along  OX,  then  after  a  time  t  has 
elapsed  there  will  be  at  a  point  P  distant  ct  from  0  a 

tangential  electric  force  equal  to  •  p  and  a  magnetic 
force  at  right  angles  both  to  0  P  and  the  electric  force, 

P       I      S7?7 

equal  to  — ^-^ — '— .      The   rate  at   which   energy  is  being 

C/x  .  C 

radiated  from  the  corpuscle  has  been  shown  by  Larmor  to 

e2   f2 
be  equal  to  -f  — ^- ;    thus  a   corpuscle   whose   velocity   is 

C 

changing  loses  energy  by  radiation. 


CHAPTER  IV. 

CORPUSCULAR    THEORY    OF    METALLIC    CONDUCTION. 

WE  now  proceed  to  apply  these  properties  of  corpuscles 
to  the  explanation  of  some  physical  phenomena ;  the 
first  case  we  shall  take  is  that  of  conduction  of  electricity 
by  metals. 

On  the  corpuscular  theory  of  electric  conduction  through 
metals  the  electric  current  is  carried  by  the  drifting  of 
negatively  electrified  corpuscles  against  the  current.  Since 
the  corpuscles  and  not  the  atoms  of  the  metal  carry  the 
current,  the  passage  of  the  current  through  the  metal  does 
not  imply  the  existence  of  any  transport  of  these  atoms 
along  the  current ;  this  transport  has  if  ten  been  looked  for 
but  never  detected.  We  shall  consider  two  methods  by 
which  this  transport  might  be  brought  about. 

In  the  first  method  we  suppose  that  all  the  corpuscles 
which  take  part  in  the  conduction  of  electricity  have  got 
into  what  may  be  called  temperature  equilibrium  with 
their  surroundings,  i.e.,  that  they  have  made  so  many 
collisions  that  their  mean  kinetic  energy  has  become  equal 
to  that  of  a  molecule  of  a  gas  at  the  temperature  of  the 
metal.  This  implies  that  the  corpuscles  are  free  not  merely 
at  the  instant  the  current  is  passing  but  that  at  this  time 
they  have  already  been  free  for  a  time  sufficiently  long  to 
allow  them  to  have  made  enough  collisions  to  have  got  into 
temperature  equilibrium  with  the  metal  in  which  they  are 
moving.  The  corpuscles  we  consider  are  thus  those 
whose  freedom  is  of  long  duration.  On  this  view  the  drift 
of  the  corpuscles  which  forms  the  current  is  brought  about 
by  the  direct  action  of  the  electric  field  on  the  free 
corpuscles. 

Second   Method. — It   is    easy   to    see,    however,   that   a 

T.M.  rc 


50  THE  COKPUSCULAK  THEORY  OF  MATTER. 

current  could  be  carried  through  the  metal  by  corpuscles 
which  went  straight  out  of  one  atom  and  lodged  at  their 
first  impact  in  another ;  such  corpuscles  would  not  be  free 
in  the  sense  in  which  the  word  was  previously  used  and 
would  have  no  opportunities  of  getting  into  temperature 
equilibrium  with  their  surroundings.  To  see  how  conduc: 
tion  could  be  brought  about  by  such  corpuscles,  we  notice 
that  the  liberation  of  corpuscles  from  the  atoms  must  be 
brought  about  by  some  process  which  depends  upon  the 
proximity  of  the  metallic  atoms.  We  see  this  because  the 
ratio  of  the  conductivity  of  a  metal  in  a  state  of  vapour  to 
the  conductivity  of  the  same  metal  when  in  the  solid  state 
is  exceedingly  small  compared  with  the  ratio  of  the  densities 
in  the  two  states.  Some  interesting  experiments  on  this 
point  have  been  made  by  Strutt,  who  found  that  when  mercury 
was  heated  in  a  vessel  to  a  red  heat,  so  that  the  pressure 
and  density  must  have  been  exceedingly  large,  the  con- 
ductivity of  the  vapour  was  only  about  one-ten  millionth  of 
the  conductivity  of  solid  mercury.  If,  however,  corpuscles 
readily  leave  one  atom  and  pass  into  another  when  the  atoms 
of  the  metal  are  closely  packed  together,  we  can  see  how  the 
electricity  could  pass  without  any  accumulation  of  free 
corpuscles.  For,  to  fix  our  ideas,  imagine  that  the  atoms 
of  the  metal  act  on  each  other  as  if  each  atom  were  an 
electric  doublet,  i.e.,  as  if  it  had  positive  electricity  on 
one  side  and  negative  on  another.  A  collection  of  such 
atoms  if  pressed  close  together  would  exert  considerable 
force  on  each  other,  and  the  force  exerted  by  an  atom  A 
on  another  B,  might  cause  a  corpuscle  to  be  torn  out  of  B. 
If  this  got  free  and  knocked  about  for  a  considerable  time 
it  would  form  one  of  the  class  of  corpuscles  previously  con- 
sidered, but  even  if  it  went  straight  from  B  into  A  it  might 
still  help  to  carry  the  current.  If  the  atoms  were  arranged 
without  any  order,  then,  though  there  might  be  interchange 
of  corpuscles  between  neighbouring  atoms,  there  would  be  no 
flux  of  corpuscles  in  one  direction  rather  than  another,  and 
therefore  no  current.  Suppose,  however,  that  the  atoms 
get  polarised  under  the  action  of  an  electric  force,  which 


THEOKY   OF   METALLIC   CONDUCTION.        51 

force  is,  say,  horizontal  and  from  left  to  right,  then  the 
atoms  will  have  a  tendency  to  arrange  themselves  so  that 
the  negative  ends  are  to  the  left,  the  positive  ones  to  the 
right.  Consider  two  neighbouring  atoms  A  and  B  (Fig.  19) : 
if  a  corpuscle  is  dragged  out  of  A  into  B  it  will  start  from 
the  negative  end  of  A  and  go  to  the  positive  end  of  B  ;  there 
will  thus  be  more  corpuscles  going  from  right  to  left  than 
in  any  other  direction  ;  this  will  give  rise  to  a  current  from 
left  to  right,  i.e.,  in  the  direction  of  the  electric  force. 

We  shall  develop  the  consequences  of  each  of  these 
theories  so  as  to  get  material  by  which  they  can  be  tested. 

A  piece  of  metal  on  the  first  of  these  theories  contains  a 
large  number  of  free  corpuscles  disposed  through  its  volume. 
These  corpuscles  can  move  freely  between  the  atoms  of  the 
metal  just  as  the  molecules  of  air  move  freely  about  in  the 


FIG.  19. 

interstices  of  a  porous  body.  The  corpuscles  come  into  colli- 
sion with  the  atoms  of  the  metal  and  with  each  other  and  at 
these  impacts  suffer  changes  in  velocity  and  momentum ; 
in  fact,  these  collisions  play  just  the  same  part  as  the 
collisions  between  molecules  do  in  the  kinetic  theory  of 
gases.  In  that  theory  it  is  shown  that  the  result  of  such 
collisions  is  to  produce  a  steady  state  in  which  the  mean 
kinetic  energy  of  a  molecule  depends  only  upon  the  absolute 
temperature  :  it  is  independent  of  the  pressure  or  the  nature 
of  the  gas,  thus  it  is  the  same  for  hydrogen  as  for  air.  We 
may  regard  the  corpuscles  as  being  a  very  light  gas,  so  that 
the  mean  kinetic  energy  of  the  corpuscles  will  only  depend 
upon  the  temperature  and  will  be  the  same  as  the  mean 
kinetic  energy  of  a  molecule  of  hydrogen  at  that  tempera- 
ture. As,  however,  the  mass  of  a  corpuscle  is  only  about 
1/1700  of  that  of  an  atom  of  hydrogen,  and  therefore  only 
about  1/3400  of  that  of  a  molecule  of  hydrogen,  the  mean 

E  2 


5<2  THE  COKPUSCULAK  THEOEY  OF  MATTEK. 

value  of  the  square  of  the  velocity  of  a  corpuscle  must  be 
3400  times  that  of  the  same  quantity  for  the  molecule  of 
hydrogen  at  the  same  temperature.  Thus  the  average  velocity 
of  the  corpuscle  must  be  about  58  times  that  of  a  molecule 
of  hydrogen  at  the  temperature  of  the  metal  in  which  the 
molecules  are  situated.  At  0°  C.  the  mean  velocity  of  the 
hydrogen  molecule  is  about  1/7  X  105  cm/sec,  hence  the 
average  velocity  of  the  corpuscles  in  a  metal  at  this 
temperature  is  about  107  cm/sec,  or  approximately  60  miles 
per  sec.  Though  these  corpuscles  are  charged,  yet  since  as 
many  are  moving  in  one  direction  as  in  the  opposite,  there 
will  be  on  the  average  no  flow  of  electricity  in  the  metal. 
The  case  is,  however,  altered  when  an  electric  force  acts 
throughout  the  metal.  Although  the  change  produced  in  the 
velocity  of  the  corpuscles  by  this  force  is,  in  general,  very 
small  compared  with  the  average  velocity  of  translation  of  the 
corpuscles,  yet  it  is  in  the  same  direction  for  all  of  them,  and 
produces  a  kind  of  wind  causing  the  corpuscles  to  flow  in  the 
opposite  direction  to  the  electric  force  (since  the  charge  on 
the  corpuscle  is  negative),  the  velocity  of  the  wind  being  the 
velocity  imparted  to  the  corpuscles  by  the  electric  force. 
If  u  is  this  velocity  and  n  the  number  of  corpuscles  per  unit 
volume  of  the  metal,  the  number  of  corpuscles  which  in  one 
second  cross  a  unit  area  drawn  at  right  angles  to  the  electric 
force  is  n  u,  and  if  e  is  the  charge  on  a  corpuscle,  the  quantity 
of  electricity  carried  through  this  area  per  second  is  n  u  e ;  this 
quantity  is  the  intensity  of  electric  current  in  the  metal ;  if 
we  denote  it  by  i,  we  have  the  equation  i  =  n  u  e.  We  now 
proceed  to  find  n  in  terms  of  X  the  electric  force  in  the 
metal.  While  the  corpuscle  is  moving  in  a  free  path  in  the 
interval  between  two  collisions,  the  electric  force  acts  upon  it 
and  tends  to  make  it  move  in  the  opposite  direction  to  itself. 
When,  however,  a  collision  occurs,  the  shock  is  so  violent 
that  the  corpuscle  moves  off  in  much  the  same  way, 
and  with  much  the  same  velocity,  as  if  it  had  not  been 
under  the  electric  field.  Thi^  the  effect  of  the  electric 
field  is,  so  to  speak,  undone  at  each  collision ;  after  the 
collision  the  electric  force  has  to  begin  again,  and  the 


THEOEY   OF   METALLIC   CONDUCTION.        53 

velocity  communicated  by  the  electric  field  to  the  corpuscle 
will  be  that  which  it  gives  to  it  during  its  free  path.  Jeans 
has  shown  that  there  is  a  slight  persistence  of  an  effect 
produced  on  a  molecule  after  an  encounter  with  another 
molecule,  that  each  collision  does  not,  as  it  were,  entirely 
wipe  out  all  the  effects  of  the  previous  history  of  the 
molecule.  To  calculate  the  amount  of  this  persistence  we 
have  to  know  the  nature  of  the  effect  we  call  a  collision ;  in 
our  case  the  effect  is  not  of  importance.  If  m  is  the  mass 
of  the  corpuscle,  the  velocity  the  corpuscle  owes  to  the 
action  of  the  electric  force  increases  uniformly  from  zero  at 

the  beginning  of  the  free  path  to  X  —  t   at    the   end,    t 

KYI 

being  the  time  between  two  collisions;  hence  the  mean 
velocity  due  to  the  force  is  -  X—  t,  and  this  is  the  velocity 

given  to  the  particles  by  the  electric  force.  If  we  care 
to  take  into  account  the  persistence  of  the  impression 
produced  by  the  electric  force  we  can  do  so  by  introduc- 
ing a  factor  ft  into  the  expression  and  saying  that 

the  average  velocity  u  due  to  the  electric  field  is  -  ft  — —  t. 

A        tn 

Unless,  however,  we  have  a  knowledge  of  the  nature  of  the 
collision  between  a  corpuscle  and  the  atom,  all  that  we  can 
determine  about  ft  is  that  it  is  a  quantity  somewhat  greater 

than  unity.     Since  u  =  —  ft t,  and  i  —  n  u  e,  we  have 

2       m 

I 


Now  unless  the  electric  force  is  enormously  large  the 
change  in  the  velocity  of  the  corpuscle  due  to  the  electric  force 
will  be  quite  insignificant  in  comparison  with  v  —  the  average 
velocity  of  translation  of  the  corpuscle.  We  may  therefore  put 
t  =  \/v,  where  A  is  the  mean  free  path  of  a  corpuscle,  hence 


0  0  A  v 

i  =-  6  n  —    -  =  -  ft  n  -  —  . 
2  m     v         2  m  v'2 

Now    in   v2  is    twice   the    average   kinetic   energy  of   a 


54  THE  CORPUSCULAK  THEORY  OF  MATTER. 

corpuscle,  and    therefore   twice   the    kinetic   energy   of   a 
molecule  of   hydrogen  at  the  same  temperature;  m  r2  is 
thus  equal  to  2  a  0  where  0  is  the  absolute  temperature  and 
2a  —  7'2  X  Hr14/273. 
From  the  relation  — 


i  =  ~ 


2  '          m  v2  4  a  6 

we  see  that  the  specific  conductivity  of  the  metal  is  equal 
to/3ne2X  v/4  a  6;  thus  the  specific  conductivity  on  this  theory 
is  independent  of  the  electric  force  X,  so  that  Ohm's  law  is 
true. 

If  the  electric  force  were  so  large  that  the  velocity 
generated  in  a  corpuscle  during  its  free  path  were  large 
compared  with  the  average  velocity  of  a  corpuscle,  the 
relation  between  current  and  electric  force  would  take  a 
different  form.  In  this  case  the  velocity  of  the  particle  is 
generated  by  the  field,  so  that  if  w  is  this  velocity  then 

-  m  w2  =  X  e  A,  or  w  =    ./    eXx--)   the  average  velocity 

/  e  v  \ 
is    one-half     of     this,    i.e.,    \/ ,    and     the     current 

v    2  in 

i  =  n  e   \/  — .    Thus  in  this  case  the  current,  instead  of 

2  m 

being  proportional  to  the  electric  force,  would  be  propor- 
tional to  the  square  root  of  it,  so  that  Ohm's  law  would  no 
longer  hold.  This  state  of  affairs  would,  however,  only 
occur  when  the  electric  force  was  exceedingly  large,  too 
large  to  be  realised  by  any  means  we  have  at  present  at  our 
command.  For  it  requires  X  e  X  to  be  large  compared  with 
the  mean  kinetic  energy  of  a  corpuscle,  which  at  0°  C. 
is  equal  to  3'6  X  1CT 14.  Now  e  is  lO"20,  thus  XX  must  be  large 
compared  with  3*6  x  106.  We  do  not  know  the  free  path 
of  a  corpuscle  in  a  metal,  but  as  the  free  path  in  air 
whose  density  at  atmospheric  pressure  is  only  1)015  is  only 
10"5  cms.,  the  free  path  in  a  metal  can  hardly  be  greater 
than  10~7  cms.  Thus  the  value  of  X  necessary  to  give  to 


THEOKY   OF   METALLIC   CONDUCTION.        55 

the  corpuscle  an  amount  of  kinetic  energy  large  compared 
with  that  it  possesses  in  virtue  of  the  temperature  of  the 
metal,  must  be  of  the  order  1014,  i.e.,  a  million  volts  per 
centimetre.  We  have  no  experimental  evidence  as  to  how 
a  conductor  would  behave  under  forces  of  this  magnitude. 

If  we  assume  that  A  is  of  the  order  1CT7  we  can  get  an 
estimate  of  n — the  number  of  corpuscles  in  a  cubic  centi- 
metre of  the  metal.  Let  us  take  for  example  silver,  whose 
specific  conductivity  is  1/1600  at  0°  C. ;  we  have,  using  the 
expression  we  have  found  for  the  conductivity — 

1         .   p  n  e*Xv  . 
1600  "4      a  B 

if  we  put  e  =  10~20,  X  =  10~7,  v  =  107,  p  =  1,  2  a  0  = 
7*2  X  10~14  we  find  n  =  9  X  1023. 

Now,  in  a  cubic  centimetre  of  silver  there  are  about 
1'6  X  1023  atoms  of  silver,  and  thus  from  this  very  rough 
estimate  we  conclude  that  even  in  a  good  conductor  like 
silver  the  number  of  corpuscles  is  a  quantity  comparable 
with  the  number  of  atoms. 

If  the  carriers  instead  of  being  corpuscles  were  bodies 
with  a  greater  mass  the  number  of  carriers  would  be  greater 
than  that  just  found.  For  we  see  from  the  preceding 
formula  that  if  the  carriers  are  in  temperature  equilibrium 
with  the  metal  n  X  v  must  be  constant  if  the  conductivity  is 
given.  Hence  if  the  mass  of  the  carriers  were  much  greater 
than  that  of  a  corpuscle  and  therefore  v  and  X  much  smaller, 
n  would  have  to  be  much  larger,  that  is,  the  number  of 
carriers  in  silver  would  have  to  be  much  greater  than  the 
number  of  atoms  of  silver,  a  result  which  shows  that  the 
mass  of  a  carrier  cannot  be  comparable  with  that  of  an  atom. 

COMPARISON  OF  THE   THERMAL  WITH   THE  ELECTRICAL 
CONDUCTIVITY. 

If  one  part  of  the  metal  is  at  a  higher  temperature  than 
another,  the  average  kinetic  energy  of  the  corpuscles  in 
the  hot  parts  will  be  greater  than  that  in  the  cold.  In 
consequence  of  the  collisions  which  they  make  with  the  atoms 


56  THE  COEPUSCULAR  THEORY  OF  MATTER. 

of  the  metal,  resulting  in  alterations  in  the  energy,  the  cor- 
puscles will  carry  heat  from  the  hot  to  the  cold  parts  of  the 
metal ;  thus  a  part  at  least  of  the  conduction  of  heat  through 
the  metal  will  be  due  to  the  corpuscles.  If  we  assume  that  the 
whole  of  the  conduction  arises  in  this  way,  we  can  find  an 
expression  for  the  thermal  conductivity  in  terms  of  the 
quantities  which  express  the  electrical  conductivity.  It  is 
proved  in  treatises  on  the  kinetic  theory  of  gases  that  k  the 
thermal  conductivity  of  a  gas  is  given  by  the  expression — 

k  =  J  n  X  v  a 

(see  Jean's  "  Kinetic  Theory  of  Gases,"  p.  259).  Here  k  is 
measured  in  mechanical  units,  and  the  effect  of  persistence 
of  the  velocities  after  the  collisions  has  been  neglected. 
Hence  to  compare  k  with  c  the  electrical  conductivity  we 
must  in  the  expression  for  the  latter  quantity  put  ft  =  1 ; 
doing  this,  we  obtain — 

n  A  v  e2 


c  = 


4  a6    ' 

hence —  ,  /    _  4  .  a2  0 

Thus  neither  n  nor  X,  the  quantities  which  vary  from 
metal  to  metal,  appears  in  the  expression  for  c/k,  so  that  the 
theory  of  corpuscular  conduction  leads  to  the  conclusion 
that  the  ratio  of  the  electrical  to  the  thermal  conductivity 
should  be  the  same  for  all  metals  and  should  vary  inversely 
as  the  absolute  temperature  of  the  metals. 

We  can  calculate  the  numerical  value  of  the  ratio  of  the 
two  conductivities  on  the  preceding  theory  as  follows  :  If  p  is 
the  pressure  of  a  gas  in  which  there  are  n  molecules  per 
cubic  centimetre,  0  the  absolute  temperature,  then — 
p  =  |  a  0  .  n ; 

hence —  a  0  __  3  p 

e         %  n  e' 

Now  e  is  the  charge  on  an  atom  of  hydrogen,  and  if  n  is 
the  number  of  hydrogen  molecules  in  a  cubic  centimetre  of 
gas  at  a  pressure  of  one  atmosphere  (i.e.,  106  dynes),  and 


THEORY  OF  METALLIC  CONDUCTION.   57 


at  0°  C.,  we  have,  since  one  electromagnetic  unit  of 
electricity  liberates  1*2  cubic  centimetres  of  hydrogen  at 
this  pressure  and  temperature— 

2'4  ne  =  I ; 
hence  at  0°  C.— 

—  =  3-6  X  106, 

e 

so  that  at  this  temperature — 

k  =  i   "2  6\   =  6-3  X  1010  in  absolute  measure. 

The  following  are  the  values  of  k/c  for  a  large  number  of 
metals  as  determined  by  Jaeger  and  Diesselhorst  in  their 
most  valuable  paper  on  this  subject : — 


Material. 

Thermal  conductivity. 

Temperature  coefficient 
of  this  ratio. 

Electrical  conductivity. 

At  18°  C. 

Per  cent. 

Copper,  commercial 

6-76  X  101() 



Copper  (1),  pure 

6-65  X  1010 

0-39 

Copper  (2),  pare 

6-71  X  1010 

0-39 

Silver,  pure        

6-86  X  1010 

0-37 

Gold  (1)  

7-27  X  1010 

0-36 

Gold  (2),  pure    

7-09  X  1010 

0-37 

Nickel 

6*99  X  1010 

0-39 

Zinc  (1)  

7'05  X  1010 

0-38 

Zinc  (2),  pure     ... 

6-72  X  1010 

0-38 

Cadmium,  pure  ... 

7-06  X  1010 

0'37 

Lead,  pure          

7-15  X  1010 

0'40 

Tin,  pure 

7'35  X  10™ 

0-34 

Aluminium 

6-36  X  1010 

0*43 

Platinum  (1)       

7*76  X  1010 

— 

Platinum  (2),  pure 

7'53  X  1010 

0-46 

Palladium 

7*54  X  1010 

0-46 

Iron  (1)   

8-02  X  1010 

0-43 

iron  (2)   

8'38  X  1010 

0-44 

Steel        ...         

9*03  X  1010 

0-35 

Bismuth... 

9-64  X  1010 

0'15 

Constantan  (60  Cu  40  Ni) 

11-06  X  1010 

0-23 

Manganine 

(84  Cu  4  Ni  12  Mn) 

9-14  X  1010 

0'27 

58  THE  CORPUSCULAR  THEORY  OF  MATTER. 


It  will  be  seen  that  the  observed  values  of  the  ratios  of  the 
thermal  and  electrical  conductivities  of  many  metals  agree 
closely  with  the  result  deduced  from  theory,  while  others 
show  considerable  deviations.  Again,  the  temperature 
coefficient  of  this  ratio  is  for  many  metals  in  agreement 
with  the  theory.  On  the  theory  the  ratio  is  proportional 
to  the  absolute  temperature ;  this  gives  a  temperature 
coefficient  of  '366  per  cent.,  and  we  see  that  for  many 
metals  the  temperature  coefficient  is  of  this  order. 

In  the  case  of  alloys  the  ratio   of   the  thermal  to  the 


Stiff* 


0.08 


007 
0.06  ^ 
0.05  5 

0.03  | 
0.02* 
0.01 
0.00 


0         10       20       30      40       SO       60        70       80        90      100 
Percentage  of  Bismuth 

FIG.  20. 

electrical  conductivity  is  not  nearly  so  constant  as  it  is  for 
pure  metals.  Even  with  alloys,  however,  any  considerable 
variation  in  the  electrical  conductivity  is  accompanied  by  a 
corresponding  variation  in  the  thermal  conductivity ;  this  is 
illustrated  by  the  curves  given  in  Fig.  20,  taken  from  a  paper 
by  Schulze  (Ann.  der  Phy.,  ix.,  p.  584),  and  which  repre- 
sent the  variations  in  both  the  electrical  and  thermal  con- 
ductivities of  alloys  of  bismuth  and  lead  with  the  percentage 
amount  of  bismuth  in  the  alloy.  It  will  be  noticed  that  the 
two  curves  are  approximately  parallel  and  have  their 
minimum  ordinate  at  about  the  same  place.  As  a  rule, 


THEORY   OF   METALLIC   CONDUCTION.        59 

although  there  are  some  exceptions,  the  ratio  of  the  thermal 
to  the  electrical  conductivity  is  larger  for  alloys  than  for 
pure  metals.  This  and  many  other  properties  of  conduc- 
tion of  electricity  through  alloys  can  be  explained  by  some 
considerations  given  by  Lord  Rayleigh  (Nature,  LIV.,  p.  154, 
"  Collected  Works,"  vol.  iv.,  p.  232).  Lord  Rayleigh  points 
out  that  in  the  case  of  a  mixture  of  metals  there  is, 
owing  to  their  thermo-electric  properties,  a  source  of 
something  which  cannot  be  distinguished  by  experiments 
from  resistance,  which  is  absent  when  the  metals  are  pure. 
To  see  this,  let  us  suppose  that  the  mixed  metals  are 
arranged  in  thin  layers,  the  adjacent  layers  being  of 
different  metals,  and  that  the  current  passes  through  the 
body  at  right  angles  to  the  faces  of  the  layer.  Now  when 
a  current  of  electricity  passes  across  the  junction  of  two 
metals  Peltier  showed  that  the  junction  was  heated  if  the 
current  passed  one  way,  cooled  if  it  passed  the  opposite 
way,  and  that  the  rate  of  heat  production  or  absorption  was 
proportional  to  the  current  passing  across  the  junction. 
Thus,  where  the  current  passes  through  the  system  of 
alternate  layers  of  the  two  metals,  one  face  of  each  layer 
will  be  cooled  and  the  other  heated,  and  thus  in  the  pile 
of  layers  differences  of  temperature  proportional  to  the 
current  will  be  established.  These  will  set  up  a 
thermoelectric  force,  tending  to  oppose  the  current, 
proportional  to  the  intensity  of  the  current.  Such 
a  force  would  produce  exactly  the  same  effect  as  a 
resistance.  Thus  in  a  mixture  of  metals  there  is,  in 
addition  to  the  resistance,  a  '  false  resistance'  due  to  thermo- 
electric causes  which  is  absent  in  the  case  of  pure  metals. 
This  false  resistance  being  superposed  on  the  other 
resistance  makes  the  electrical  resistance  of  alloys  greater 
than  the  value  indicated  by  the  preceding  theory.  This 
result  gives  an  explanation  of  the  fact  that  the  ratio  of  the 
thermal  to  the  electrical  resistance  is  greater  for  alloys  than 
it  is  for  pure  metals. 

The  experiments  of  Dewar  and  Fleming  on  the  effect  of 
very  low  temperatures  on  the  resistance  of  pure  metals  and 


60  THE  COKPUSCULAK  THEOEY  OF  MATTER. 

alloys  show  that  there  is  a  fundamental  difference  between 
the  resistances  of  pure  metals  and  mixtures,  for  while  the 
resistance  of  pure  metals  diminishes  uniformly  as  the 
temperature  diminishes  and  would  apparently  vanish  not 
far  from  the  absolute  zero  of  temperature,  the  resistance  of 
alloys  gives  no  indication  of  disappearing  at  these  very  low 
temperatures,  but  apparently  tends  to  a  finite  limit. 

The  electrical  conductivity  of  a  metal  is  proportional  to  n 
the  number  of  free  corpuscles  per  unit  volume.  Now,  since 
a  free  corpuscle  will  continually  be  getting  caught  by  and 
attached  to  an  atom,  the  corpuscles,  when  the  metal  is  in  a 
steady  state,  must  be  in  statical  equilibrium  ;  the  number 
of  fresh  corpuscles  produced  in  unit  time  being  equal  to  the 
number  which  disappear  by  re-combination  with  the  atoms 
in  the  same  time.  We  should  expect  the  number  of 
re-combinations  in  unit  time  to  be  proportional  to  the 
number  of  collisions  in  that  time,  i.e.,  to  n\r\  where  r  is 
the  interval  between  two  collisions  ;  r  is  equal  to  \/v  where 
A  is  the  free  path  and  v  the  velocity  of  the  corpuscle. 
Hence  the  number  of  re-combinations  in  unit  time  will  be 

equal  to  y  -r-  where  7  represents  the  proportion  between 

the  number  of  collisions  which  result  in  re-combination  and 
the  whole  number  of  collisions.  If  q  is  the  number  of 
corpuscles  produced  per  cubic  centimetre  per  second,  we 
have  when  there  is  statical  equilibrium— 


Thus  c  the  electrical  conductivity  of  a  metal  is  expressed 
by  the  equation  — 


c  =      . 


4  y      a  B 

For  most  pure  metals  the  conductivity  is  inversely  pro- 
portional to  the  absolute  temperature  0,  hence  we  conclude 
that  q  A2  must  be  independent  of  the  temperature.  Now 
we  should  not  expect  A.  to  vary  more  rapidly  with  the 
temperature  than  the  distance  between  two  molecules,  a 


THEOEY   OF   METALLIC   CONDUCTION.        61 

quantity  whose  variation  with  the  temperature  is  of  the 
same  order  as  that  of  the  linear  dimensions  of  the  body,  and 
therefore  represented  by  the  coefficient  of  thermal  expansion, 
a  very  small  quantity ;  thus,  since  q  A2  is  independent  of 
the  temperature,  and  X2  only  varies  slowly  with  the 
temperature,  the  variations  of  q  with  temperature  can 
only  be  slight,  hence  we  conclude  that  the  dissociation  of 
the  atom  which  produces  the  corpuscles  cannot  to  any 
considerable  extent  be  the  effect  of  temperature. 

We  should  expect  to  have  fewer  free  corpuscles  and 
therefore  smaller  conductivity  in  a  salt  of  the  metal  than 
in  the  metal  itself.  For  in  the  salt  the  atoms  of  the  metal 
are  all  positively  electrified  and  have  already  lost  corpuscles, 
which  have  found  a  permanent  home  on  the  atoms  of  the 
electro-negative  element.  From  the  positively  electrified 
metal  atoms  corpuscles  will  find  it  difficult  to  escape,  and 
the  rate  of  production  of  free  corpuscles  will  be  very  much 
lower  than  in  the  pure  metal,  where  in  addition  to  positively 
electrified  atoms  neutral  and  negatively  electrified  atoms  of 
the  metal  are  present. 

LORENTZ  THEORY  OF  EADIATION. 

Kadiation  of  heat  may  be  produced  by  the  impact  of 
corpuscles.  When  a  corpuscle  comes  into  collision  with  an 
atom  it  experiences  rapid  changes  in  its  velocity,  and 
therefore  will,  as  explained  on  p.  46,  emit  pulses  of  intense 
electric  and  magnetic  force ;  the  thickness  of  these  pulses 
will  be  the  distance  traversed  by  light  during  the  time 
occupied  by  a  collision.  Thus,  if  we  consider  any  atom  of 
the  metal,  it  will  be  from  time  to  time,  as  the  corpuscles 
strike  against  it,  the  centre  of  pulses  of  intense  electric  and 
magnetic  force.  These  forces  at  a  point  near  the  atom 
will  vary  in  a  very  abrupt  manner.  A  pulse  of  intense 
electric  force,  lasting  for  a  very  short  time,  will  pass  over 
the  point,  then  there  will  be  an  interval  in  which  the 
electric  force  disappears,  and  again,  after  the  space  of  time 
between  two  collisions,  another  intense  pulse  will  pass  over 


62  THE  COEPUSCULAR  THEOEY  OF  MATTEE. 

the  point.  Now  though  the  electric  force  jumps  about  in 
this  abrupt  way,  we  know  by  the  theorem  due  to  Fourier 
that  it  can  be  represented  as  the  sum  of  a  number  of  terms, 
each  of  which  is  of  the  form  cos  (pt  +  e)  where  t  represents 
the  time.  Each  of  these  terms  represents  a  harmonic  wave 
of  electric  force,  and  by  the  electro-magnetic  theory  of  light 
a  harmonic  wave  of  electric  force  is  a  wave  of  light  or  radiant 
heat.  Thus  we  can  represent  the  irregular,  jerky  electric 
field  produced  by  the  collision  as  arising  from  the  super- 
position of  a  number  of  waves  of  light  or  radiant  heat,  and 
if  we  can  calculate  the  amplitude  of  vibration  of  the  dis- 
turbance of  any  period,  we  can  calculate  at  once  the  energy 
in  the  light  of  this  period  emitted  by  one  molecule,  and 
therefore,  by  summation,  by  the  metal. 

Of  the  whole  group  of  waves  which  represent  the  electric 
field  due  to  the  collisions,  Lorentz  has  shown  how  to  calculate 
the  amplitudes  of  those  whose  wave  length  is  very  large 
indeed  compared  with  the  free  path  of  the  corpuscles,  and 
has  shown  that  the  energy  in  the  vibrations  whose  fre- 
quency is  between  q  and  8q  given  out  per  second  per  unit 
of  area  of  a  plate  where  thickness  is  A  is  equal  to — 

TT  e2  n  X  v  ; 

c  represents  the  velocity  of  light,  e  the  charge  on  the 
corpuscle,  A  the  mean  free  path  of  a  corpuscle,  and  v  its 
mean  velocity  of  translation.  This  represents  the  rate  at 
which  the  body  emits  energy.  To  find  the  amount  of 
energy  of  this  frequency  present  in  the  body  when  the 
radiation  is  in  a  steady  state,  we  must  take  into  account  the 
absorption  of  this  energy  in  its  course  through  the  body. 
For  imagine  a  body  built  up  of  piles  of  parallel  plates ; 
then  if  there  were  no  absorption  the  energy  emitted  by  the 
most  distant  portions  would  reach  any  point  Q,  and  if  the 
size  of  the  body  were  infinite  the  amount  of  energy  per  unit 
volume  at  Q  would  be  infinite  also.  If,  however,  there  was 
strong  absorption,  so  that  the  radiation  was  practically  all 
absorbed  in  the  space  of  one  millimetre,  then  it  is  evident 


THEOEY  OF   METALLIC   CONDUCTION.        63 

that  the  portions  of  the  body  whose  distance  from  Q  is  more 
than  one  millimetre  will  not  send  any  energy  to  Q,  and  how- 
ever large  the  body  may  be  the  energy  at  Q  will  be  finite. 
When  the  energy  in  the  body  has  settled  down  into  a  steady 
state,  the  energy  given  out  by  any  portion  must  be  equal  to 
the  amount  acquired  by  absorption.  This  principle  enables 
us  to  find  the  amount  of  energy  per  unit  volume  of  the  body 
when  the  radiation  is  in  a  steady  state.  The  absorption  of 
these  very  long  waves  in  a  conductor  is  due  to  the  same 
cause  as  the  production  of  heat  in  the  conductor  when  an 
electric  current  passes  through  it,  since  these  waves  are  made 
up  of  electric  and  magnetic  forces.  When  an  electric  force  X 
acts  on  a  conductor  and  produces  an  electric  current  whose 
intensity  is  i,  the  rate  at  which  energy  is  absorbed  per  unit 
volume  is  Xi,  or  if  o-  is  the  specific  resistance  of  the  con- 
ductor the  rate  at  which  energy  is  absorbed  is  equal  to  X*/<r, 
since  o-i  =  X.  We  must  express  this  in  terms  of  E  the  energy 
per  unit  volume  in  the  conductor.  One  half  of  this  energy 
is  due  to  the  electric  field,  the  other  half  to  the  magnetic 
field  which  accompanies  it ;  the  energy  per  unit  volume  due 

X2 

to  the  electric  field  is   - — ^-,  c  being  the  velocity  of  light 

X1 
through  the  medium,  hence  E  =  ^ %,  and  X2  =  4  TT  c2  E, 

hence  X2/o-  the  rate  at  which  energy  is  absorbed  per  unit 
volume  is  equal  to — 


and  the  rate  per  unit  area  of  a  plate  of  thickness  A  is— 

4  TT  ca  E  A 

V 

Now  in  a  steady  state  the  energy  emitted  is  equal  to  the 
energy  absorbed ;  the  expression  for  the  rate  at  which 
energy  is  emitted  is  given  on  p.  62 ;  equating  this  to  the 
rate  at  which  the  energy  is  absorbed,  we  have — 

4.0^A    =    Ag^g^  (1) 

O-  6   7T2   C 


64     THE    CORPUSCULAR   THEORY   OF   MATTER. 

but  (see  p.  56)— 

1      _  e2  X  n  v 

IT    '          4  a  0 

when    0  is   the   absolute   temperature.      Substituting   this 
value  for  l/o-,  equation  (1)  becomes  — 

c,  E  (e»  A  „  ,-)    =  £dq  e,nx  v_  (2) 

4  a  6  6  7T2  c 

The  quantities  n  and  A  which  differentiate  one  substance 
from  another  occur  in  the  same  form  on  both  sides  of  the 
equation  :  one  side  expresses  the  absorption,  the  other  the 
radiation,  and  we  see  that  the  ratio  of  the  two  is  inde- 
pendent of  the  nature  of  the  substance.  Hence  this  view 
of  radiation  would  explain  Kirchhoff's  law  that  good  radia- 
tors are  also  good  absorbers.  Dividing  out  the  common 
factors  from  equation  (2),  we  get  — 


or  if  A  is  the  wave  length  of  the  vibration  whose  frequency 
is  q  we  have,  since  — 


and  this  is  the  expression  for  the  amount  of  energy  per 
unit  volume  whose  wave  length  is  between  X  and  d  X  when 
the  absolute  temperature  is  0.  This  expression  does  not 
involve  any  constant  which  depends  upon  the  nature  of 
the  body,  hence  it  would  be  the  same  at  the  same  tempera- 
ture for  all  bodies.  The  expression  for  E  is  of  the  type 

/XA  0)  —g-  ,  where/  (A  0)  denotes  a  function  of  A  and  6.    The 

A 

researches  of  Wien  have  shown  that  it  is  only  a  formula  of 
this  type  which  fits  in  with  the  values  of  the  radiation 
observed  by  him  and  others  in  experiments  with  bodies  at 
different  temperatures.  The  preceding  expression  is  of  the 
type  suggested  by  Lord  Rayleigh  (Phil.  Mag.,  June,  1900). 
Since  a  6  represents  the  mean  kinetic  energy  of  any  gas 


THEORY  OF   METALLIC   CONDUCTION.        65 

at  the  absolute  temperature  0,  we  can  calculate  the  value 
of  a,  and  thus  arrive  at  a  numerical  estimate  of  the  amount 
of  radiation  given  by  the  preceding  expression.  If  we  find 
this  coincides  with  the  observed  amount  it  will  be  a  strong 
confirmation  of  the  theory. 

By  the  kinetic  theory  of  gases,  if  p  is  the  pressure, 
N  the  number  of  molecules  per  unit  volume  of  the  gas — 

p  =  ~  N  mv2, 

hence  ^  mv2,  the  mean  kinetic  energy  of  a  particle,  is  equal 
to  3  p/2  AT,  but  J  m  r2  =  a  0,  hence— 

aO=^. 

2Ar 

Now  at  the  pressure  of  760  millimetres  of  mercury  and 
a  temperature  of  0°  C.,  p  =  106,  6  =  273,  and  N=  4  X  1019, 
hence  a  =  1*32  X  10~16.  Assuming  that  the  radiation  is 
expressed  by  equation  (1),  we  can  use  the  equation  if  we 
know  the  amount  of  radiation  to  find  a,  and  Lorentz  finds 
from  the  experiments  made  by  Lummer  and  Pringsheim  and 
Kurlbaum  on  the  amount  of  radiation  given  out  by  hot  bodies 
that  a  =  1'2  X  10~16.  Thus  the  argument  between  theory 
and  the  results  of  experiment  is  very  satisfactory  and  gives 
us  considerable  confidence  in  the  truth  of  the  theory.  It 
ought,  however,  to  be  pointed  out  that  we  should  get  the 
same  expression  for  the  radiant  energy  E,  whatever  may 
be  the  mass  or  charge  of  the  moving  electrified  bodies, 
which  are  supposed  to  generate  this  energy  by  their  col- 
lisions and  absorb  it  by  their  motion  in  the  electric  field, 
provided  that  the  mean  kinetic  energy  of  these  bodies  had  the 
same  value  as  that  we  have  assumed  for  the  corpuscles. 

The  energy  calculated  in  this  way  by  Lorentz  is  only  a 
part  of  the  energy  radiated  in  consequence  of  the  collisions. 
It  is  that  part  which,  when  the  electric  forces  produced  by 
the  collisions  is  expressed  by  Fourier's  method  as  the  sum 
of  a  number  of  harmonic  components,  corresponds  to  the 
part  of  the  disturbance  which  can  be  expressed  by  the 

T.M.  F 


66  THE  COBPUSCULAK  THEORY  OF  MATTER. 

terms  with  exceedingly  long  wave  lengths.  But  the  dis- 
turbance, as  we  have  seen,  consists  in  a  succession  of 
exceedingly  thin  pulses,  the  thickness  of  the  pulse  being 
comparable  with  the  distance  passed  over  by  light  in  the 
time  occupied  by  a  collision,  while  the  part  calculated  by 
Lorentz  is  only  the  part  which  can  be  represented  by 
harmonic  terms  whose  wave  length  is  long  compared  with 
the  distance  passed  over  by  light,  not  in  the  short  space 
occupied  by  a  collision,  but  in  the  much  longer  interval 
which  elapses  between  two  collisions.  It  is  evident  that 
Lorentz's  investigation  leaves  out  of  consideration  a  large 
part  of  the  radiation,  and  that  this  part,  arising  from  the 
accumulation  of  a  number  of  thin  pulses,  will  be  analogous 
to  the  Rontgen  rays — that,  in  fact,  they  will  be  Rontgen 
rays,  mainly  of  a  very  absorbable  type,  since  the  corpuscles 
which  produce  them  are  moving  much  more  slowly  than 
the  cathode  rays  in  the  ordinary  Rontgen  ray  bulb.  In 
fact,  a  mathematical  investigation  leads  us  to  the  con- 
clusion that,  of  the  energy  radiated  at  a  collision,  there 
will  be  more  of  this  type  than  the  long  wave  type  calculated 
by  Lorentz.  The  character  of  the  radiation  will  depend 
upon  the  time  taken  by  a  collision  between  the  corpuscle 
and  a  molecule,  if  this  time  is  so  short  that  the  distance 
travelled  by  light  during  the  collision  is  very  small 
compared  with  the  wave  length  of  light  in  the  visible  part 
of  the  spectrum,  then  the  resulting  radiation  will  be  of  the 
Rontgen  ray  type  and  not  visible  light.  If,  however,  the 
time  of  collision  is  so  prolonged  that  light  during  this  time 
can  travel  over  a  distance  comparable  with  the  wave  length 
of  light  in  the  visible  part  of  the  spectrum,  then  the 
resulting  radiation  will  be  visible  light,  and  the  maximum 
intensity  of  this  light  will  be  in  that  part  of  the  spectrum 
where  the  wave  length  is  comparable  with  the  distance 
travelled  by  light  during  a  collision,  i.e.,  when  the  period 
of  vibration  of  the  light  is  comparable  with  the  time  of 
a  collision.  The  intensity  of  light  having  smaller  wave 
lengths  than  this  will  rapidly  fall  off  as  the  wave  length 
diminishes.  Thus  in  the  case  of  these  prolonged  collisions 


THEOEY   OF   METALLIC   CONDUCTION.        67 

the  radiation  would  be  ordinary  light,  the  intensity  rising 
to  a  maximum  at  a  particular  part  of  the  spectrum  and 
then  diminishing  rapidly  in  the  region  of  smaller  wave 
lengths.  These  are  characteristic  properties  of  the  radiation 
emitted  by  a  black  body.  We  know,  however,  the  character 
of  the  radiation  from  such  a  body  depends  only  upon  the 
temperature  and  not  at  all  upon  the  nature  of  the  body, 
thus  the  colour  of  the  light  at  which  the  intensity  of  the 
radiation  is  a  maximum  depends  only  on  the  temperature 
moving  towards  the  blue  end  of  the  spectrum  as  the 
temperature  is  increased.  On  the  theory  that  this  radiation 
arises  from  the  collision  of  corpuscles  the  wave  length 
where  the  intensity  of  the  radiation  is  a  maximum  depends 
on  the  duration  of  the  collision ;  hence,  if  the  radiation 
from  hot  substances  arises  in  the  way  we  have  supposed, 
the  duration  of  a  collision  between  a  corpuscle  and  a 
molecule  of  the  substance  must  be  independent  of  the 
nature  of  the  substance  and  depend  only  upon  the 
temperature,  and  the  higher  the  temperature  the  shorter 
must  be  the  duration  of  the  collision. 

By  the  application  of  the  Second  Law  of  Thermodynamics 
it  has  been  shown  that  when  the  body  is  at  the  absolute 
temperature  6  the  amount  of  energy  in  the  part  of  the 
spectrum  comprised  between  wave  lengths  X  and  X  +  d  X 
must  be  of  the  form  X~5  $  (X  0)  d  X;  where  ^  is  a  function 
which  cannot  be  determined  by  thermodynamical  principles 
alone.  The  mathematical  theory  of  the  production  of 
radiation  by  collisions  shows  that  this  energy  is  given  by 

an  expression  of  the  form  X~5  F  (^-7-,)  d  X  where  T  is 

the  duration  of  the  collision  V  the  velocity  of  light  and 
F  represents  a  function  whose  form  depends  upon  the 
nature  of  the  forces  exerted  during  the  collision.  Comparing 
these  two  expressions  we  see  that  T  must  be  conversely 
proportional  to  0,  that  is,  inversely  proportional  to  the 
square  of  the  velocity  of  the  corpuscles.  The  velocity  of 
corpuscles  at  0°  C.  when  in  temperature  equilibrium  with 
their  surroundings  is  about  107  cm./sec.,  the  wave  length  at 

p  2 


68  THE  CORPUSCULAR  THEORY  OF  MATTER. 

which  the  intensity  is  greatest  at  0°  C.  is  about  10 ~3  cm. 
In  a  Rontgen  ray  bulb  giving  out  hard  rays  the  velocity  of 
the  corpuscles  may  be  about  1010  cm. /sec.,  or  103  times  the 
velocity  of  those  in  the  metal ;  hence,  if  the  law  of  duration 
of  impacts  is  true,  the  radiation  produced  by  the  impact  of 
the  corpuscles  in  the  tube  should  be  a  maximum  for  a  wave 
length  of  10-3/10°  or  10 "9  cm.,  as  this  is  of  the  same  order 
as  the  thickness  of  a  pulse  of  very  penetrating  Rontgen 
radiation ;  this  test,  as  far  as  it  goes,  confirms  the  law  of 
the  duration  of  collisions. 

THE  EFFECT   OF  A  MAGNETIC  FIELD  ON  THE  FLOW  OF  AN 
ELECTEIC  CURRENT  :    THE    "  HALL  EFFECT." 

Hall  found  that  the  lines  of  flow  of  an  electric  current 
through  a  metallic  conductor  are  distorted  when  the  con- 
ductor is  placed  in  a  magnetic  field.  The  distortion  is  of 
the  character  which  would  be  produced  if  an  additional 
electromotive  force  were  to  act  at  right  angles  to  the 
original  one  producing  the  current,  and  also  at  right 
angles  to  the  magnetic  force.  Thus  if  a  horizontal 
electromotive  force  producing  a  current  from  right  to  left 
acts  on  a  thin  piece  of  metal  in  the  plane  of  the  paper,  if 
the  plate  is  placed  in  a  magnetic  field  whose  lines  of  force 
are  at  right  angles  to  the  plane  of  the  paper  and  down- 
wards, the  current  is  distorted  as  if  a  small  vertical  electro- 
motive force  in  the  plane  of  the  paper  acted  upon  the 
metal.  In  some  metals — for  example,  bismuth  and  silver — 
this  force  would  be  vertically  upwards ;  in  others,  such  as 
iron,  cobalt,  and  tellurium,  the  force  would  be  vertically 
downwards.  In  some  alloys  it  is  said  that  the  force  is  in 
one  direction  for  small  magnetic  forces  and  in  the  opposite 
direction  for  large  ones.  In  many  cases  it  is  not  propor- 
tional to  the  magnetic  force.  The  theory  of  electric  con- 
duction we  have  been  considering  would  indicate  a 
distortion  of  the  lines  of  flow  of  a  current  by  a  magnetic 
field,  as  the  following  considerations  will  show. 

Suppose   a   current   of   electricity  flows   from   right   to 
left    through    the    plate.       This,    on    the    view    of    the 


THEORY   OF  METALLIC   CONDUCTION.        69 

current  previously  taken,  indicates  that  the  negative  cor- 
puscles have,  on  the  average,  a  finite  velocity  from  left  to 
right.  Let  the  average  value  of  this  velocity  of  drift  of  the 
negative  corpuscles  be  u.  If  a  magnetic  force  downwards 
at  right  angles  to  the  plate  acts  on  these  corpuscles,  they 
will  be  acted  on  by  a  vertically  upward  force  in  the  plane 
of  the  paper,  equal  numerically  to  Heu,  where  e  is  the 
magnitude  of  the  charge  on  the  corpuscle,  and  H  is  the 
intensity  of  the  magnetic  force.  The  force  on  the  corpuscle 
is  the  same  as  if  there  were  an  electromotive  force  acting 
vertically  downwards  in  the  plane  of  the  paper.  Thus,  there 
would  be  a  distortion  of  the  lines  of  flow  of  the  same  sign 
and  character  as  the  Hall  effect  in  bismuth.  If,  however, 
this  were  a  complete  representation  of  the  action  of  the 
magnetic  field  on  the  current,  the  Hall  effect  would  be  of 
the  same  sign — the  sign  it  has  for  bismuth — in  all  metals, 
and  would  always  be  proportional  to  the  magnetic  force  ; 
neither  of  these  statements  is  true.  Inasmuch  as  the  Hall 
effect  would  be  of  the  opposite  sign,  if  the  carriers  of  the 
electricity  through  the  metal  were  positively  charged  par- 
ticles instead  of  negatively  charged  ones,  some  physicists, 
in  order  to  explain  the  existence  of  Hall  effects  of  opposite 
signs,  have  assumed  that  electricity  is  carried  through  metals 
by  two  types  of  carriers,  one  positively  the  other  negatively 
electrified ;  in  some  metals  the  negative  carriers  are  pre- 
dominant, in  others  the  positive.  There  are,  I  think,  two 
very  serious  objections  to  this  assumption.  In  the  first 
place  we  have  no  evidence  of  the  existence  of  positively 
electrified  particles  able  to  thread  their  way  with  facility 
through  metals,  and  in  the  second  place  the  assumption 
does  not  explain  the  various  phenomena  connected  with  the 
Hall  effect.  It  would  indeed  explain  the  existence  of  Hall 
effects  of  different  signs,  but  on  this  hypothesis  the  amount 
of  the  Hall  effect  would  be  proportional  to  the  magnetic 
force,  which  is  by  no  means  the  case  for  all  substances. 

The  complexity  of  the  laws  of  the  Hall  effect  suggests 
that  it  is  due  to  several  causes,  but  we  can,  without  calling 
in  the  aid  of  positively  charged  carriers  of  electricity,  see 


70     THE   CORPUSCULAR   THEORY   OF   MATTER, 

other  sources  for  the  variation  in  sign,  and  the  failure  to 
be  directly  proportional  to  the  magnetic  force.  In  the  pre- 
ceding investigation  we  have  considered  merely  the  effect  of 
the  magnetic  force  on  the  particle  during  its  free  path,  and 
have  neglected  any  influence  of  the  magnetic  force  on  the 
collisions  between  the  corpuscles  and  the  molecules. 
"We  can,  however,  easily  see  how  a  magnetic  field  might 
make  suitable  molecules  arrange  themselves  so  that  they 
produce  a  rotatory  effect  on  the  motion  of  a  corpuscle  when 
the  corpuscle  came  into  collision  with  the  molecule,  and 
that  the  sign  of  this  effect  might  in  some  cases  be  the  same 
as,  in  others  opposite  to,  the  rotation  produced  by  the 
magnetic  field  when  the  corpuscle  was  travelling  over  its 
free  path.  Thus — to  take  a  simple  instance — imagine  a  body 
whose  molecules  are  little  magnets  ;  then  if  the  body  is 
placed  in  a  magnetic  field  such  that  the  lines  of  force  are 
vertical  and  downwards,  the  molecules  of  the  body  will 
arrange  themselves  so  that  their  axes  tend  to  be  vertical, 
the  negative  poles  being  at  the  top,  the  positive  at  the 
bottom.  Then  close  to  the  magnet,  in  the  region  between 
its  poles,  the  lines  of  force  due  to  the  magnet  will  be 
in  the  opposite  direction  to  those  due  to  the  magnetic 
field,  and  the  intensity  of  the  force  close  in  to  the  magnet 
may  be  very  much  greater  than  that  of  the  external  field. 
In  this  case  when  the  corpuscle  came  into  collision  with  a 
molecule  the  velocity  would  be  rotated  in  the  opposite 
direction  to  its  rotation  by  the  magnetic  field  before  it  came 
into  collision  with  the  magnet,  i.e.,  while  it  was  travelling 
over  its  mean  free  path.  In  this  case  the  expression  for 
the  Hall  effect  would  consist  of  two  terms,  one  arising  from 
the  free  path,  the  other  from  the  collisions,  and  these  terms 
would  be  of  opposite  signs.  If  the  molecules  were  small 
portions  of  a  diamagnetic  substance  it  is  easy  to  see  that 
the  effect  due  to  the  collisions  would  be  of  the  same  sign  as 
that  due  to  the  free  path.  It  is  perhaps  worthy  of  note 
that,  with  the  exception  of  tellurium,  which  has  quite  an 
abnormal  value,  the  substance  for  which  the  Hall  effect  has 
the  largest  negative  value,  calling  the  free  path  effect 


THEORY   OF   METALLIC   CONDUCTION.        71 

positive,  is  iron.  It  would  be  interesting  to  see  if  in 
exceedingly  strong  magnetic  fields,  much  stronger  than  those 
required  to  saturate  the  iron,  the  Hall  effect  would  change 
sign. 

We  must,  however,  I  think,  be  careful  not  to  import  from 
the  kinetic  theory  of  gases  ideas  about  the  free  paths  of 
corpuscles  which  may  not  be  applicable  in  the  case  of 
metals.  The  study  of  metals  by  means  of  micro-photo- 
graphy has  shown  that  their  structure  is  extremely  complex. 
This  is  illustrated  by  Fig.  21,  which  represents  the 
appearance  under  the  microscope  of  a  piece  of  cadmiun 


FIG.    21. 

when  polished  and  stained.  A  piece  of  metal  apparently 
consists  of  an  assemblage  of  a  vast  number  of  small  crystals, 
and  the  appearance  of  the  metal  when  strained  past  the  limit 
of  perfect  elasticity  shows  that  under  strain  these  crystals 
can  slip  past  each  other.  The  structure  of  a  piece  of  metal 
is  thus  quite  distinct,  from  that  of  a  gas,  where  the  particles 
are  distributed  at  equally  spaced  intervals.  In  a  metal,  on 
the  other  hand,  it  would  seem  that  the  molecules  of  the 
metal  are  collected  in  clusters,  each  cluster  containing 
several  molecules,  and  that  the  metal  is  built  up  of  aggre- 
gates of  such  clusters.  The  collisions  which  determine  the 
free  path  of  a  corpuscle  may  be  with  these  clusters  and  not 


72  THE  COKPUSCULAK  THEORY  OF  MATTER. 

with  the  individual  molecules,  and  if  this  were  so,  large 
variations  in  the  free  path  might  be  brought  about  by 
variations  in  the  number  of  molecules  in  each  cluster  with- 
out any  variation  of  corresponding  magnitude  in  the  density 
of  the  metal.  Thus,  to  take  a  simple  case,  suppose  that  the 
clusters  are  little  spheres,  and  let  us  compare  the  free  paths  of 
a  corpuscle  (1)  when  there  are  n  spheres  of  radius  a  per  unit 
volume  ;  and  (2)  when  there  are  in  spheres  of  radius  b,  the 
amount  of  matter  per  unit  volume  being  the  same  in  the 
two  cases,  so  that  n  a3  =  in  b3.  If  AI  and  A2  are  respectively 
the  free  paths  in  the  two  cases,  then— 

i 
and      A2  =. 


m  TT 
and  since  n  a3  =  in  b3  we  have — 

Ai/A,  =  a/b. 

So  that  in  this  case  the  free  path  would  be  proportional 
to  the  radius  of  the  cluster.  Thus  the  bigger  the  cluster 
the  longer  the  free  path.  It  follows  that  if  a  rise  in  tem- 
perature caused  the  clusters  to  break  up  to  some  extent  and 
become  smaller,  it  would  produce  a  considerable  diminution 
in  the  free  path  of  a  corpuscle  without  any  marked  change 
in  the  density,  whereas  in  a  gas  a  rise  in  temperature  unac- 
companied by  a  change  in  density  would,  if  the  collisions 
between  the  molecules  of  a  gas  were  like  those  between 
hard  elastic  spheres,  produce  no  change  in  the  free  path. 
If  the  theory  of  conduction  of  electricity  by  corpuscles  in 
temperature  equilibrium  with  their  surroundings  is  true,  we 
must,  I  think,  suppose  that  there  is  large  variation  of  the 
free  path  with  the  temperature  and  with  the  nature  of  the 
metal.  We  shall  see  Irom  the  consideration  of  the  Peltier 
effect  that  the  number  of  free  corpuscles  per  unit  volume 
does  not,  in  general,  vary  greatly  from  one  metal  to  another; 
so  that  the  very  large  variations  in  the  electrical  resistance 
of  metals  must  arise  much  more  from  variations  in  the  free 
paths  of  the  corpuscles  than  from  variations  in  the  number 
of  corpuscles.  Hence  the  ratio  of  the  free  paths  of  the 


THEOKY  OF   METALLIC   CONDUCTION.        73 

corpuscles  will  be  of  the  same  order  as  the  ratio  of  their 
conductivities  for  electricity.  Now,  if  the  free  paths  of  the 
corpuscles  in  the  metal  were  determined  by  the  same  con- 
siderations as  in  a  gas,  i.e.,  if  A  were  to  be  equal  to  N/TT  a2, 
N  being  the  number  of  molecules  per  unit  volume,  and 
a  the  radius  of  the  molecules,  we  can  show  that  the  varia- 
tions in  A  would  not  be  nearly  large  enough  to  explain  the 
variation  in  the  electrical  conductivity.  For  we  can  deter- 
mine N  by  dividing  the  density  of  the  metal  by  its  atomic 
weight,  and  we  can  get  some  information  as  to  the  value  of 
#3  from  the  values  of  the  refractive  indices  of  compounds  of 
the  different  metals.  Doing  this,  we  find  that  the  variations 
in  1/N  TT  a2  are  not  nearly  so  large  as  the  variations  in  the 
electric  conductivity,  and  that  there  is  little,  if  any, 
correspondence  between  these  quantities.  Moreover,  if 
the  theory  we  are  discussing  is  correct  there  must  not 
merely  be  large  variations  in  the  value  of  A.  for  the  different 
metals,  but  even  in  the  same  metal  at  different  tempera- 
tures. This  follows  from  the  consideration  of  the  Thomson 
effect,  i.e.,  the  convection  of  heat  by  an  electric  current  flowing 
along  an  unequally  heated  conductor. 


PELTIEK  DIFFERENCE  OF  POTENTIAL  BETWEEN  METALS. 

Suppose  that  we  place  two  metals  A  and  B,  which  are  at 
the  same  temperature,  in  contact,  and  that  the  pressure  of 
the  corpuscles  (i.e.,  J  N  m  v2  where  N  is  the  number  of 
corpuscles  in  unit  volume,  m  the  mass,  v  the  mean  velocity 
of  the  corpuscles)  in  A  is  greater  than  that  in  B.  Then  cor- 
puscles will  flow  from  A  to  B  ;  but  as  these  corpuscles  are 
negatively  charged,  the  flow  of  corpuscles  will  charge  B 
negatively  and  A  positively.  The  attraction  of  the  positive 
electricity  in  A  will  tend  to  prevent  the  corpuscles  escaping 
from  it,  and  the  flow  will  cease  when  the  attraction  of  the 
positive  electricity  in  A  and  the  repulsion  of  the  negative  in 
B  just  balances  the  effect  of  the  difference  in  pressure.  The 
positive  electrification  in  A  and  the  negative  in  B  will  be 
close  to  the  surface  of  separation,  and  these  two  electrifications 


74  THE  COKPUSCULAK  THEOKY  OF  MATTER. 

will  produce  a  difference  in  electric  potential  between  A  and 
B,  which  we  can  calculate  in  the  following  way. 

Let  us  suppose  that  there  is  a  thin  layer  between  the 
substances  A  B,  in  which  the  transition  from  A  to  B  takes 
place  gradually.  Let  N  be  the  number  of  corpuscles 
per  unit  volume  at  a  point  distant  x  from  one  of  the 
boundaries  of  this  layer,  p  the  pressure  of  the  corpuscles 
at  this  point,  and  X  the  electric  force.  Then  if  e  is  the 
charge  on  a  corpuscle,  the  force  acting  on  the  corpuscles 
per  unit  volume  is  X  Ne.  This,  when  there  is  equilibrium, 
must  be  balanced  by  the  force  arising  from  the  variation 
in  pressure  as  we  pass  from  one  side  of  the  layer  to  the 

C\  *Y) 

other.     The  force  due  to  the  pressure  is  —  ^-,  hence  — 

a  x 

±£  =  XNe. 
a  x 

But  if  &  is  the  absolute  temperature  — 


hence,  if  the  temperature  is  constant  across  the  layer,  we 
have  — 

2      /»  l  dN        v 
Za6NTx=Xe' 

Integrating  both  sides  of  this  equation  across  the  layer, 
we  get— 

2    a    B    ,  Ni  jr 

3TlogA2=T' 

where  V  is  the  difference  in  potential  between  the  two  sides 
of  the  layer  and  A^  and  Nz  are  the  numbers  of  corpuscles  per 
unit  volume  in  A  and  B  respectively.  Thus  in  crossing 
the  junction  of  two  metals  there  will,  unless  the  number  of 
corpuscles  in  the  two  metals  is  the  same,  be  a  finite  change 
in  potential.  Now  f  a  Oje  =p/Ne,  and  since  it  is  the  same 
for  all  gases  we  may  take  the  case  of  hydrogen  at  0°  C. 
and  atmospheric  pressure  for  which  p  =  106,  and  Ne  =  '41  ; 
thus  at  0°  C.  f  a  6/e  =  2'5  X  10H,  so  that  in  volts— 


THEORY   OF   METALLIC   CONDUCTION.        75 

The  potential  differences  which  arise  in  this  way  are  not 
comparable  with  the  volta  differences  of  potential  between 
metals  in  contact,  for  to  produce  a  potential  difference  of 
one  volt,  log  Ni/N*  =  40,  or  A\/.V2  =  2'36  X  1017 — a  result 
quite  incompatible  with  the  comparative  values  of  the 
resistances  of  two  such  metals  as  copper  and  zinc.  Com- 
paratively small  variations  in  the  number  of  corpuscles 
would,  however,  produce  potential  differences  quite  com- 
parable with  those  measured  by  the  Peltier  effect,  i.e.,  the 
heating  or  cooling  of  the  junction  of  two  metals  when  an 
electric  current  passes  across  them.  Thus,  to  take  a  case 
where  the  Peltier  effect  is  exceptionally  large,  that  of 
antimony  and  bismuth,  whose  V  at  0°  C.  is  about  1/30  of 
a  volt,  we  see  from  equation  (1)  that  for  these  metals 
log  (NJNJ  =  1-33,  or  N^N*  =  3'8.  Thus,  if  the  number  of 
corpuscles  in  the  unit  volume  of  antimony  were  about 
four  times  that  in  bismuth  we  should,  on  this  theory,  get 
Peltier  effects  of  about  the  right  amount.  Since  the  Peltier 
effect  for  antimony  and  bismuth  is  very  much  larger  than 
that  for  most  pairs  of  metals,  we  see  that  the  theory 
indicates  that  in  general  the  number  of  free  corpuscles 
per  unit  volume  does  not  vary  much  from  one  metal  to 
another.  From  the  Peltier  effects  of  each  metal  with  a 
standard  metal  we  can  get  the  ratio  of  the  number  of 
corpuscles  in  these  metals  to  the  number  in  the  standard 
metal.  Having  done  this,  since  at  the  same  temperature 
the  conductivity  of  the  metals  is  proportional  to  the  pro- 
duct of  the  number  of  corpuscles  per  unit  volume  and  the 
free  path  of  a  corpuscle  in  the  metal,  we  can  get  the  ratio 
of  the  free  paths  in  the  different-  metals,  and  we  can  then 
see  whether  the  free  paths  obtained  in  this  way  can  be 
reconciled  with  the  other  properties  of  the  metals.  The 
result  of  such  a  comparison  leads,  I  think,  to  the  con- 
clusion that  the  mechanism  by  which  we  have  supposed 
the  electric  current  to  be  conveyed  through  a  conductor  is 
at  most  only  a  part  and  not  the  whole  of  the  process  of 
metallic  conduction.  One  reason  for  this  conclusion  is  the 
large  changes  which  take  place  in  the  electrical  resistance 


76  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

of  some  metals  at  fusion,  changes  which  do  not  seem  to  be 
accompanied  by  any  corresponding  change  in  their  thermo- 
electric quality.  Thus  the  conductivities  of  tin,  zinc  and 
lead  at  their  melting  points  are;  when  the  metals  are  in  the 
solid  state,  about  twice  what  they  are  in  the  liquid.  These 
metals  all  contract  on  solidification,  so  that  the  average 
distance  between  the  molecules  is  greater  in  the  liquid 
than  in  the  solid  state.  The  electrical  conductivity  varies 
as  the  product  of  N  the  number  of  corpuscles  per  unit 
volume,  and  A  the  free  path  of  a  corpuscle.  Since  the 
distance  between  the  molecules  is  greater  in  the  liquid 
than  in  the  solid  state,  we  should  expect  the  free  path  of 
the  corpuscles  to  be  greater,  but  if  NI  A:  and  N2  A2  are 
respectively  the  values  of  N  A  in  the  solid  and  liquid  states, 
NI  A!  =  2  A72  A2,  and  since  A2  is  greater  than  A1?  A\  must  be 
greater  than  2  AT2.  A  reference  to  equation  (1)  will  show 
that  this  involves  a  Peltier  effect  between  the  solid  and  the 
liquid  metal  of  about  half  the  magnitude  of  that  between 
bismuth  and  antimony,  and  thus,  as  these  effects  go, 
exceedingly  large.  Now  Fitzgerald,  Minarelli  and  Ober- 
meyer,  as  quoted  by  G.  Wiedemann,  "  Elektricitat,"  ii.,  p.  289, 
could  detect  no  sudden  change  in  thermo-electric  circuits 
with  these  metals  when  they  passed  from  the  solid  to  the 
liquid  state,  whereas  if  the  number  of  free  corpuscles  had 
diminished  to  one  half,  the  effect  would  have  been  very 
conspicuous.  There  is  thus  a  discrepancy  between  the 
results  of  the  determination  of  the  relative  number  of 
corpuscles  in  the  two  states  by  data  derived  (1)  from 
thermo-electric  phenomena;  (2)  from  their  electric  resistance. 
This  discrepancy  is  so  large  that  it  is  impossible  to  suppose 
it  is  due  to  any  errors  in  the  data  derived  from  experiment. 

THE  THOMSON  EFFECT. 

Lord  Kelvin  showed  that  in  some  metals  an  electric 
current  carries  heat  from  the  hot  to  the  cold  parts  of  the 
metal,  while  in  other  metals  the  transference  of  heat  is  in 
the  opposite  direction.  Let  us  calculate  what  this  trans- 
ference of  heat  would  be  on  the  theory  we  are  discussing. 


THEORY   OF   METALLIC   CONDUCTION.        77 

Let  A  B  be  a  bar  of  metal,  and  let  the  temperature 
increase  from  A  to  B.  If  the  pressure  of  the  corpuscles 
depends  upon  the  temperature  there  must  be  electromotive 
forces  along  the  bar  to  keep  the  corpuscles  from  drifting 
under  these  pressure  differences.  If  p  is  the  pressure  of 
the  corpuscle  at  a  point  distant  x  from  the  end  A,  then  the 
force  acting  on  the  corpuscles  included  between  two  planes 
at  distances  x,  x  -f  A#,  from  A,  is,  per  unit  area  of  these 

planes,  equal  to  A  x  •—-  and  acts  from  right  to  left.     To 
cl  x 

balance  this  we  must  have  an  electromotive  force  X  tending 
to  move  the  corpuscles  from  left  to  right,  determined  by 
the  equation  — 

v  d  p  ,. 

A  e  n  A  x  =  —±~  A  x 
cl  x 

or-  Xe  =  -1  *£, 

n  d  x 

where  n  is  the  number  of  corpuscles  per  unit  volume  at  a 
distance  x  from  A.  If  0  is  the  absolute  temperature  of  the 
bar  at  A  we  have  (see  page  65)  — 


hence — 


p   =  £  n  a  6. 


21    d    , 

—  —    —  (an  0). 
on  d  x 


Hence  a  corpuscle  in  travelling  from  x  +  8  x  to  x  will 
abstract  from  the  metal  an  amount  of  heat  whose  mechanical 
equivalent  is  X  e  8  x,  or — 

2  1    d 

-  —  (an  &)  d  x. 

3  n  d  x 

The  corpuscle  when  at  x  +  d  x  has  an  amount  of  kinetic 

energy  equal  to  a  ( 0  +  <j—dx\  while  at  xits  kinetic  energy 
\         (t  x     / 

is  reduced  to  a  0,  hence  the  corpuscle  will  communicate  to 
the  metal  between  x  and  x  +  d  x  an  amount  of  heat  equal 


78  THE  CORPUSCULAR  THEORY  OF  MATTER. 

to  a-r—  dx;  thus  the  total  amount  of  heat  communicated  by 
dx  J 

the  corpuscle  to  the  metal  is — 

d  0         2  1    d  A}', 

a  —   -  _  (a  n  0}  j-  d  x, 

d  x         6  n  d  x  ) 


or — 


(a  —  ?   1  A  (an  6)}  d  0. 
V         3  n  d  0  J 


If  the  current  i  is  flowing  in  the  direction  in  which  x 
increases,  the  number  of  corpuscles  which  cross,  unit  area 
in  unit  time,  in  the  opposite  direction  to  the  current 
is  i/e,  and  the  mechanical  equivalent  of  the  heat  they 
communicate  to  the  metal  between  the  places  where  the 
temperatures  of  the  metal  are  respectively  6  and  0  +  d  0  is 
equal  to  — 

if         2  1    d  ,.\  j  a 

—  (  a  —  —  -  —  (a  n  0}  }  d  6. 
e\         3  n  d  6  v         JJ 

But  if  o-  is  the  "  specific  heat  of  electricity  in  the  metal," 
this  amount  of  heat  is  by  definition  equal  to— 

—  i  a-  dO 

the   minus    sign    being  inserted    because  the    current    is 

flowing  from    the    cold    to  the  hot  part  of    the  circuit; 
hence  — 

1    /          2  1     d     ,  fr\ 

a-  =   —  -    (a—    _  ~  —-  (a    n    V)  ) 

e    \          3  n  d  0  J 

-  "' 


The  term  ^—  in  the  expression  for  a-  is  the  same  for  all 

metals,  and  since  the  electro-motive  force  round  a  thermo- 
electric circuit  consisting  of  two  metals  only  involves  the 
difference  of  the  specific  heats  of  electricity  in  the  metals, 
this  term  will  not  affect  the  electromotive  force  round  the 


THEOEY   OF   METALLIC   CONDUCTION.        79 

circuit.  It  will,  however,  affect  the  amount  of  heat 
developed  in  the  conductor,  and  we  shall  find  that  unless 

this  term  is  very  nearly  balanced  by  the  term  -^  - — ?—  log  n 

o    e   d  u 

the  amount  of  heat  developed  by  the  flow  of  a  current 
through  an  unequally  heated  conductor  would  be  far 
greater  than  the  amount  actually  observed. 

For  a/3e  is  about  0'45  X  104,  so  that  the  amount  of 
heat  expressed  by  the  first  term  in  equation  (1)  developed  by 
a  unit  current  in  flowing  between  two  places  where  the 
temperature  differed  by  1°  C.  would  equal  *45  X  104/4'2  X 
107,  or  T07  X  10~4  calories  per  second. 

The  metal  in  which  this  heat  effect  is  largest  is,  as  far  as 
our  present  knowledge  extends,  bismuth,  and  for  this 
metal  the  observed  effect  is  only  about  *3  X  10  ~4  calories, 
or  about  1/3  of  the  amount  expressed  by  the  term  a/3  e, 
and  the  effect  in  bismuth  is  very  much  greater  than  in  any 
other  metal ;  hence  since  o-  is  small  compared  with  a/3  e,  we 
have  by  equation  (1) 

log  n  —  r  log  0  +  a  constant 

2 

approximately,  so  that  approximately  n  will  vary  as 
0s,  i.e.,  the  number  of  free  corpuscles  will  vary  approxi- 
mately as  the  square  root  of  the  absolute  temperature.  If 
the  specific  heat  of  electricity  is  positive  the  number  of 
free  corpuscles  will  vary  a  little  more  rapidly  than  this 
with  the  temperature.  If  the  specific  heat  is  negative  it 
will  vary  a  little  less  rapidly.  This  variation  of  the 
number  of  free  corpuscles  with  the  temperature  involves  a 
still  more  rapid  variation  of  the  mean  free  path.  For 
(see  p.  54)  we  have  seen  that  the  electrical  conductivity  is 
proportional  to  n  A.  v  /  6.  Now  v  is  proportional  to  $  and  n, 
as  we  have  just  seen,  varies  approximately  according  to  the 
same  law,  hence  the  electrical  conductivity  is  approximately 
proportional  to  A.  the  free  path  of  the  corpuscles  in  the 
metal.  But  for  many  pure  metals  the  electrical  con- 
ductivity varies  approximately  as  the  reciprocal  of  the 


80  THE  CORPUSCULAR  THEORY  OF  MATTER. 

absolute   temperature ;    hence  for  these  metals  the  mean 
free  path  must  also  vary  with  the  temperature  in  the  same 
way,  i.e.,  be  inversely  proportional  to  the  absolute  tempera- 
ture.     This   rapid   variation   of   the   free   path    with    the 
temperature  would  not  be  possible  if  the  structure  of  the 
metal  were  analogous  to  that  of  a  gas  compressed  so  that 
the  distances  between  the  molecules  were  all  diminished  in 
the    same  proportion.      We  have  seen  that  if  the  metal 
consisted  of  aggregations  of  molecules  which  broke  up  to 
some    extent    as    the  temperature     rose,    we    might   get 
a  rapid  variation  of  the  mean  free  path,  with  the  tempera- 
ture.     Since    the    free    path,   according   to    this    theory, 
varies    approximately   as  the   reciprocal   of    the   absolute 
temperature,    the    free    paths    at    the    low    temperatures 
which  can  be  obtained  by  the  use  of  liquid  air  or  liquid 
hydrogen    ought   to   be   much    greater  than    at  ordinary 
laboratory  temperatures.     Thus  the  effects  which  depend 
on  the  free  path,  such  as  the  effect  of  magnetic  force  on 
electrical   resistance,  or   the  absorption    of    light    by  the 
metal  (which  should  vary  greatly  according  as  the  time  of 
vibration    of    the  light  is  greater    or  less  than  the  time 
occupied  by  a  corpuscle  to  describe  its  free  path),  would  be 
greatly    affected    by    the   lowering   of    the    temperature : 
experiments  on  these  points  would  be  valuable  tests  of  the 
theory.     If  X  varies  as  1/0,  X/v  the  time  occupied  by  a  cor- 
puscle in  describing  its  free  path  will  vary  as  1/0*.     The 
velocity  acquired  by  a  corpuscle  under  a  constant  electric 
force  will  also  vary  as  l/0i,  and  will  thus  diminish  rapidly 
as  the  temperature  increases. 

THE  NUMBER  OF  FREE  CORPUSCLES  IN  UNIT  VOLUME 
OF  THE  METAL. 

We  can  determine  from  the  amount  of  heat  absorbed  or 
developed  when  a  current  of  electricity  passes  across  the 
junction  of  two  metals,  the  ratio  of  the  number  of  cor- 
puscles in  unit  volume  of  the  two  metals,  and  from  the 
Thomson  effect  we  can  determine  the  change  in  this 
number  for  any  one  metal  with  the  temperature.  Hence, 


THEORY  OF   METALLIC   CONDUCTION.        81 


if  we  can  determine  the  number  of  corpuscles  ^er  unit 
volume  in  any  one  metal  at  any  one  temperature,  we  can 
deduce  the  number  in  any  other  metal  at  any  temperature. 

We  shall  now  pass  on  to  the  consideration  of  methods 
to  determine  the  absolute  number  of  corpuscles  per  unit 
volume  ;  since  the  electrical  conductivity  gives  us  the  value 
of  n  X,  a  method  of  determining  A  will  also  lead  to  the 
determination  of  n.  We  shall  begin  with  those  methods 
which  lead  to  the  direct  determination  of  n. 

One  of  the  simplest  of  these  in  principle  is  founded  on  the 
consideration   of    what    takes   place    when    a    charge   of 
electricity  is  communicated  to  a  piece  of  metal.     Let  us,  to 
fix  our  ideas,  suppose  that  the  charge  is  a  negative  one  and 
that  it  is  carried  by  free  corpuscles.     These  corpuscles  must 
occupy   a  layer  of  finite  thickness  at  the  surface  of  the 
metal,  for  if  the  layer  were  reduced  to  infinitesimal  thick- 
ness the  pressure  exerted  by  these  corpuscles  would  be  vastly 
greater  than  the  pressure  exerted  by  the  corpuscles  in  the 
interior  of  the  metal,  and  the  consequence  would  be  that 
corpuscles   would  diffuse  from  the  layer  into  the  interior 
of  the  metal.     The  corpuscles  will  diffuse  until  the  electric 
force  exerted  by  their  charges  is  just  able  to  balance  the 
forces  arising  from  the  difference  of  pressure  between  the 
surface  and  the  interior.     We  can  calculate  the  thickness  of 
the  layer  occupied  by  the  negative  charge  in  the  following 
way  :     Let  A  be  the  face  of  a  flat  piece  of  metal  having  a 
negative  charge  ;  let  n  be  the  number  of  corpuscles  per 
unit  volume  before  the  charge  was   communicated  to  the 
metal,  n  +  £  the  number  at  a  point  at  a  distance  01  from  the 
surface  of  the  plate  after  the  charge  was  communicated, 
p  the  pressure  of  the  corpuscles  at  this  distance,  and  X  the 
electric  force  tending  to  stop  the  corpuscles  from  moving 
from  left  to  right.      Then  when  the  corpuscles  have  got 
into  a  steady  state  — 

£=>•>>«. 

but  p  =  §  a  (n  +  £)  0,  where  a   0  is  the  mean    kinetic 

T.M.  G 


82  THE  COEPUSCULAE  THEOEY  OF  MATTER. 

energy  of  a  corpuscle  at  the  absolute  temperature  0,  and 
since  n  does  not  depend  upon  x,  we  have,  assuming  that  $ 
is  small  compared  with  n  — 

*0.**=Xe«> 

8          dx 

but—  dX 

^  =  4^> 

if  e  is  measured  in  electrostatic  units,  hence  — 
2         ft  £ 


or—  £  —  A  e~px 

A  2 

where  p2  =     (J  e  ™  and  4  is  a  constant.    To  find  A  we  have 

s  a  6 
^oo 

£  j  0    £dx  =  Q,itQisthe  charge  per  unit  area  ;  hence 

e  A 
substituting  for  £,  -   -  =  Q,  or 


Thus  the  value  of  £  is  appreciable  until  x  is  large  com- 
pared with  1/p;  we  may  thus  take  1/p  or  (a  0/6  ?r  e2  ?/)*  as 
the  measure  of  the  thickness  of  the  layer  occupied  by  the 
electricity  ;  substituting  for  a.0  and  e  the  values  3'6  X  lO"14 
and  3  X  1Q-10,  we  find  that,  at  0°  C., 

1  (  ]* 


P 

/ 

Now  since  — 

dX 

dx  ~ 

4 

we  have  — 

X=    47T 

Q 

p 

This  is  the  difference  in  potential  between  the  surface  and 
a  point  in  the  interior,  hence  we  see  that  if  we  communicate 
a  charge  of  electricity  to  a  hollow  conductor  whose  surface 


THEOEY  OF  METALLIC  CONDUCTION.   83 

is  kept  at  zero  potential,  the  interior  of  that  conductor  will 
not,  as  is  usually  assumed  in  electrostatics,  remain  at  zero 
potential,  but  will  change  by  4  TT  Q/p  where  Q  is  the  charge 
per  unit  area  of  the  conductor.  Hence,  if  we  measure  the 
change  produced  by  a  known  charge  we  shall  determine  p 
and  hence  n  by  the  equation  15  TT  n  =  106  p".  If  the  number 
of  corpuscles  is  comparable  with  the  number  of  molecules 
of  the  metal,  which  we  may  take  as  between  1022  and  1023, 
p  will  be  comparable  with  108,  and  so  the  thickness  of  the 
layer  through  which  the  electricity  is  distributed  will  be  of 
the  order  of  10  ~8  cm.  In  this  case  the  change  in  the 
potential  of  the  interior  produced  by  any  feasible  charge 
will  be  small,  but  not  perhaps  too  small  to  be  measurable. 
If  the  conductor  were  exposed  to  air  at  atmospheric  pressure 
the  greatest  value  of  4  ?r  Q  possible  without  sparking  would 
be  100  in  electrostatic  measure.  By  embedding  the  con- 
ductor in  a  solid  dielectric,  such  as  paraffin,  we  could 
probably  increase  4  TT  Q  to  1000  without  discharge.  If  4  -n-  Q 
is  103  and  p  =  108,  the  change  in  potential  would  be  10~5  in 
electrostatic  measure,  or  3  X  10~3  of  a  volt,  and  this  ought 
to  be  capable  of  measurement. 

Experiments  have  been  made  by  Bose  and  others  to  see  if 
the  electrical  resistance  would  be  altered  by  giving  a  charge 
of  electricity  to  a  very  thin  conductor ;  so  far  these  have  led 
to  negative  results.  We  might  at  first  sight  expect  that  if 
we  increased  the  supply  of  negative  corpuscles  by  com- 
municating a  charge  of  negative  electricity  to  the  strip  of 
metal  we  should  increase  the  conductivity  ;  but  this  need 
not  necessarily  be  the  case,  for  suppose  the  surface  instead 
of  being  flat  were  corrugated,  then  the  charge  would  be  all 
at  the  tops  of  the  corrugations ;  but  this  would  be  quite  out 
of  the  way  of  a  current  flowing  through  the  film,  which  would 
take  the  short  circuit  through  the  base  of  the  corrugations. 
As  the  electricity  only  penetrates  a  distance  comparable  with 
the -size  of  a  molecule,  it  is  impossible  to  avoid  an  effect  of 
this  kind,  however  carefully  the  surface  is  polished. 

We  can,  however,  find  both  lower  and  upper  limits  to  the 
number  of  free  corpuscles,  and  as  these  limits  lead  to 

G  2 


84  THE  COKPUSCULAK  THEORY  OF  MATTEE. 

contradiction  we  shall,  after  investigating  them,  proceed  to 
the  consideration  of  the  question  whether  the  other  view 
of  the  function  and  disposition  of  the  corpuscles  alluded  to 
on  page  49  is  less  open  to  objection. 

We  can  obtain  a  lower  limit  to  the  number  of  free 
corpuscles  per  unit  volume  of  a  metal  by  the  consideration 
of  the  results  of  the  experiments  of  Eubens  and  Hagen  on 
the  reflection  of  long  waves  from  the  surface  of  metals.  It 
follows  from  these  experiments  that  the  electrical  con- 
ductivity of  metals  when  waves  whose  length  equals  25  /*, 
//.  being  10~4  cm.,  pass  through  them  is  the  same  as  the 
conductivity  under  steady  electrical  forces,  and  that  even 
when  the  waves  are  as  short  as  4  /x,  the  electrical  conductivity 
is  within  about  20  per  cent,  of  that  for  steady  forces.  "We 
can  easily  show  that  if  k  is  the  conductivity  under  steady 
forces ;  then  when  the  forces  vary  as  sin  n  t  the  conductivity 

sin?  n  T 
will  be  proportional  to  k  — a  rj^   ,  where  2  T  is  the  interval 

/€/        -/. 

between  two  collisions.  Thus,  unless  this  interval  be  small 
compared  with  the  period  of  the  electric  force  the  con- 
ductivity will  be  very  materially  reduced.  Thus  if  T  were 
as  great  as  one  quarter  of  the  period  of  the  force,  so  that 

n  T  =  ^,  the  conductivity  would  be  reduced  to  l/(7r/2)2,  or  '4 

of  its  steady  value.  As  the  diminution  of  the  conductivity 
for  light  waves  whose  length  is  4  /x  is  less  than  this,  we 
conclude  that  the  interval  between  two  collisions  is  less 
than  one-quarter  the  period  of  this  light,  or  less  than 
3'3  X  1Q-15  sec.  Hence  u  the  velocity  under  unit  electric 

force,   since    it    is    equal   to   ~  —    T,    will  be   less   than 

2  m 

p 

\  3'3  X  10'15— ,  and  since  k  the  conductivity  is  n  e  u,  n 

flfYL 

k  1015  m 
will  be  greater  than  k/eu,  i.e.,  than  2  . 

JL  O  v 

For  silver  k  is  about  5  X  10 "4,  and  since  e/m  =  1*7  X  107 
and  e  =  10~20,  we  see  that  n  for  this  metal  must  be  greater 
than  1-8  X  1024. 


THEOKY  OF   METALLIC   CONDUCTION.        85 

It  is  this  result  which  leads  to  the  difficulty  to  which  we 
have  alluded,  for  if  there  were  this  number  of  corpuscles 
per  unit  volume,  then,  since  the  energy  possessed  by  each 
corpuscle  at  the  temperature  6  is  a  0,  the  energy  required 
to  raise  the  temperature  of  the  corpuscles  in  unit  volume 
of  the  metal  by  1°  C.  is  n  a,  and  since  a  =  T5  X  10~16 
(see  page  65),  the  energy  which  would  have  to  be  communi- 
cated to  unit  volume  of  the  silver  to  raise  the  temperature 
of  the  corpuscles  alone  would  be  greater  than  1/3  X  1*8 
X  108  ergs.,  or  about  6  gram  calories.  But  to  raise  the 
temperature  of  a  cubic  centimetre  of  silver  one  degree,  only 
requires  about  0*6  calories,  and  this  includes  the  energy 
required  to  raise  the  temperature  of  the  atoms  of  the  metal 
as  well  as  that  of  the  corpuscles.  We  thus  get  to  a  con- 
tradiction. The  value  of  the  specific  heats  of  the  metals 
shows  that  the  corpuscles  cannot  exceed  a  certain  number, 
but  this  number  is  far  too  small  to  produce  the  observed 
conductivities  if  the  intervals  between  the  collisions  are  as 
small  as  is  required  by  the  behaviour  of  the  metals  in 
Eubens'  experiments. 


CHAPTER  V. 

THE    SECOND    THEORY    OF    ELECTRICAL    CONDUCTION. 

WE  shall  now  proceed  to  develop  the  second  theory  of 
electrical  conductivity  and  see  whether  it  is  as  successful  in 
explaining  the  relation  between  the  thermal  and  electrical 
conductivities  as  the  other  one,  and  whether  or  not  it  is 
open  to  the  same  objections. 

On  this  theory  the  corpuscles  are  supposed  to  be  pulled 
out  of  the  atoms  of  the  metal  by  the  action  of  the  surrounding 
atoms.  In  order  to  get  a  sufficiently  definite  idea  of  this 
process  to  enable  us  to  calculate  the  amount  of  electrical 

0©  0©  00  0©  0©  0® 


FIG.    22. 

conductivity  which  it  would  produce,  we  shall  suppose  that 
in  the  metal  there  is  a  large  number  of  doublets,  formed  by 
the  union  of  a  positively  electrified  atom  with  a  negatively 
electrified  one,  and  that  the  interchange  of  corpuscles  takes 
place  by  a  corpuscle  leaving  the  negative  component  of  one 
of  these  doublets  and  going  to  the  positive  constituent  of  the 
other.  Under  the  action  of  the  electric  force  these  doublets 
tend  to  arrange  themselves  along  that  line  in  the  way 
indicated  in  Fig.  22,  much  in  the  same  way  as  the  Grot  thus 
chains  in  the  old  theory  of  electrolysis.  The  corpuscles 
moving  in  the  direction  of  the  arrows  will  give  rise  to  a 
drift  of  negative  electricity  against  the  direction  of  the 
electric  force  or  a  current  of  positive  electricity  in  the  same 
direction  as  the  force. 

We  now  proceed  to  calculate  the  magnitude  of  the  current 


THEOKY   OF   ELECTKICAL   CONDUCTION.      87 

produced  in  this  way.  Consider  a  doublet  formed  by  a 
charge  of  electricity  +  e>  connected  with  another  charge  —  e, 
and  placed  in  an  electric  field  where  the  intensity  of  the 
electric  force  is  X.  The  potential  energy  of  the  doublet, 
when  its  axis  (the  line  joining  the  negative  to  the  positive 
charge)  makes  an  angle  0  with  the  direction  of  the  electric 
force,  is  —  X  e  d  cos  0,  where  d  is  the  distance  between  the 
charges  in  the  doublet.  If  the  doublets  distribute  them- 
selves as  they  would  in  a  gas  in  which  the  distribution  of 
potential  energy  follows  Maxwell's  law,  the  number  pos- 
sessing potential  energy  V  will  be  proportional  to  e-/(  F, 
where  1/h  =  f  a  0,  ad  being  as  before  the  mean  kinetic  of  a 
molecule  at  the  absolute  temperature  e.  Then  the  number 
of  doublets  whose  axes  make  an  angle  between  0  and  0  -}-  dB 
with  the  direction  of  X,  is  proportional  to  ehXedcose  sin  6  d  6, 
and  the  average  value  of  cos  0  for  these  doublets  is  equal  to 

^Xedcose  cos  6  sinOd  6 


Now  Xe  dli  will,  unless  the  electric  force  greatly  exceeds 
the  value  it  has  in  any  ordinary  case  of  metallic  conduction, 
be  exceedingly  small,  for  the  potential  difference  through 
which  the  charge  e  must  fall  in  order  to  acquire  the  energy 
possessed  by  a  molecule  at  the  temperature  0°  C.,  is  about 
1/25  of  a  volt,  and  h  is  proportional  to  the  reciprocal  of 
this  energy,  thus  unless  the  electric  field  is  so  strong  that 
there  is  in  the  space  between  the  two  components  of  the 
doublet  a  fall  of  potential  comparable  with  this,  h  Xe  d  will 
be  small.  But  when  this  is  so  — 

f  ^  Xe  d  cos6  cos  9  sin  0  d  0  =  -  h  X  c  d 
J  o  3 

and—  f  thXedcose  sin  8  dO  =  2, 

•'  o 

1  2  Xed 

hence  the  mean  value  of  cos  6  is  ^  h  X  e  d,  or  -  -^-. 

If  each  doublet  discharges  a  corpuscle  p  times  a  second  ,  then 


88  THE  CORPUSCULAK  THEORY  OF  MATTER. 

in  consequence  of  the  polarisation  we  have  just  investigated, 
the  resultant  flow  of  corpuscles  will  be  the  same  as  if  each 
doublet  discharged  a  corpuscle  parallel  but  in  the  opposite 

direction  to  the  electric  force  p  X  g  — .-  times  per  second. 

Hence,  if  n  is  the  number  of  doublets  per  unit  volume,  b  the 
distance  between  the  centres  of  the  doublets,  the  current 
through  unit  area  will  be  equal  to — 

2  e~  X  d  p  n  b 
9          a  6 

If  we  assume  that  the  orientation  of  the  axes  of  the 
doublets  in  a  metal  follows  the  same  law  as  in  a  gas,  this 
will  be  the  expression  for  the  current  through  the  metal, 
hence  c  the  electrical  conductivity  will  be  given  by  the 
expression — 

_  2  e2  d  p  n  b 

~  9  a<9 

THERMAL  CONDUCTIVITY. 

If  we  suppose  that  the  kinetic  energy  of  the  corpuscle  in 
a  doublet  is  proportional  to  the  kinetic  energy,  i.e.,  to  the 
temperature  of  the  doublet,  the  interchange  of  corpuscles 
will  carry  heat  from  the  hot  parts  of  the  metal  to  the  cold, 
and  will  thus  give  rise  to  the  conduction  of  heat.  Let  us 
suppose  that  the  kinetic  energy  of  a  corpuscle  when  in 
a  doublet  at  temperature  6  is  a  6.  If  the  corpuscle  goes 
from  a  doublet  where  the  temperature  is  0  +  8  0  to  one  where 
the  temperature  is  0,  it  will,  when  the  latter  doublet  has 
lost  a  corpuscle  to  make  way  for  the  one  coming,  have 
caused  a  transference  of  heat  equal  to  a  8  0.  Consider 
now  the  transference  of  heat  across  a  plane  at  right  angles 
to  the  temperature  gradient.  The  number  of  corpuscles 
crossing  this  plane  in  unit  time  is  equal  to  J  n  b  .  p.  If  the 
difference  of  temperature  between  the  adjacent  doublets 
is  8  6,  this  will  transfer 

~  n  b  p  a  8  0 

o 


THEORY  OF   ELECTRICAL   CONDUCTION.     89 

units  of  heat  across  the  plane  in  unit  time,  but  as  b  is  the 

distance  between  the  doublets  80=—    b,    where   x   is 

ct  oc 

measured  in  the  direction  of  the  flow  of  heat.     Hence  *  the 
thermal  conductivity  is  given  by  the  equation — 

K  =  -  ntfpa. 

Thus  on  this  theory  K/C,  the  ratio  of  the  thermal  to  the 
electrical  conductivity  is  equal  to — 

3  ba?0 
2   UTi?' 

On  the  theory  discussed  before  this  ratio  was  equal  to — 

4  a2  9 


In  a  substance  in  which  the  doublets  are  so  numerous  as 
to  be  almost  in  contact,  d  and  b  will  be  very  nearly  equal 
to  each  other,  and  in  this  case  the  ratio  of  the  conductivities 
on  the  new  theory  would  be  to  that  on  the  old  in  the  pro- 
portion of  9  to  8.  When  the  doublets  are  more  sparsely 
disseminated  b  will  be  greater  than  d  and  the  ratio  of  the 
conductivities  given  by  the  new  theory  will  be  greater  than 
that  given  by  the  old.  The  agreement  between  theory 
and  the  results  of  experiment  is  at  least  as  good  in  the 
new  theory  as  in  the  old,  for  the  new  theory  gives  for  good 
conductors  results  of  the  right  order  of  magnitude,  while 
the  presence  of  the  factor  b/d  indicates  that  the  ratio  is  not 
an  absolute  constant  for  all  substances  but  varies  within 
small  limits  for  good  conductors  and  wider  ones  for  bad 
ones.  All  this  is  in  agreement  with  experience. 

THEORY  OF  CONNECTION  BETWEEN  RADIANT  ENERGY  AND  THE 
TEMPERATURE. 

We  have  seen  (p.  61)  that  Lorentz  has  shown  that 
the  long  wave  radiation  can  be  regarded  as  a  part  of  the 


90  THE  CORPUSCULAR  THEORY  OF  MATTER. 

electromagnetic  pulses  emitted  when  the  moving  cor- 
puscles come  into  collision  with  the  atoms  of  the  substance 
through  which  they  are  moving,  and  he  has  given  an 
expression  for  the  amount  of  the  energy  calculated  on 
this  principle,  which  agrees  well  with  that  found  by 
experiment.  But  in  the  new  theory,  as  in  the  old,  we  have 
the  sudden  starting  and  stopping  of  charged  corpuscles  and 
therefore  the  incessant  production  of  electromagnetic  pulses ; 
these  when  resolved  by  the  aid  of  Fourier's  theorem  will 
be  represented  by  a  series  of  waves,  having  all  possible 
wave  lengths  from  zero  to  infinity.  We  must  see  if  the 
energy  in  the  long  wave  length  radiation  at  a  given 
temperature  would  on  the  new  theory  be  approximately 
equal  to  that  on  the  old. 

It  will  be  necessary  to  examine  a  little  more  closely  than 
we  have  hitherto  done  the  theory  of  the  radiation  from  metals 
due  to  the  stopping  and  starting  of  electrified  systems 
inside  the  metal.  We  have  already  (see  p.  64)  quoted  an 
expression  due  to  Lorentz  for  the  amount  of  the  very  long 
wave  length  radiation  due  to  the  stopping  of  corpuscles. 
We  can,  however,  by  the  following  method,  obtain  an 
expression  for  the  energy  corresponding  to  any  wave  lengths 
emitted  by  unit  volume  of  the  metal.  In  the  case  of  very 
long  waves  this  expression  coincides  with  that  given  by 
Lorentz. 

We  have  seen  that  when  the  motion  of  an  electrified 
particle  is  accelerated  it  gives  off  pulses  of  electric  and 
magnetic  force.  If  /  is  the  acceleration  of  a  charged  body 
O,  at  the  time  t,  the  magnetic  force  at  a  point  P  at  a  time 

i    O  P     •    e  f  sin  6     ,          „  .     ;1 
t  +  -    -  ,  is — —  where  6  is  the  angle  OP  makes  the 

0  C      \J  Jr 

direction  of  the  acceleration,  and  c  the  velocity  of  light. 
The  energy  per  unit  volume  at  P  due  to  this  magnetic  field 

is  equal  to  ~  where  H  =  e -f  8™  6,  and  the  amount  of 

O   7T  C      OP 

this  energy,  which  flows  out  radially  through  unit  area  at 
P,  is  c  H2 1 8  TT.  Integrating  over  the  surface  of  the  sphere 
with  centre  0  and  radius  OP  we  find  that  the  flow  of  energy 


THEOEY  OF   ELECTRICAL   CONDUCTION.      91 

1  e2  f2 

due  to  the  magnetic  field  is,  in  unit  time  7  — — .     There  is 

o    c 

an  equal  flow  of  energy  due  to  the  electric  field,  hence  the 
rate   at   which   the   charged   body  is  radiating  energy  is 

2     6'2  f 2 

— ,  a  result  first  given  by  Larmor. 
The  total  amount  of  energy  radiated  is 

if /:.>*• 

When  we  know  /  as  a  function  of  t  we  can  find  the  total 
amount  of  energy  radiated.  If  we  wish  to  find  how  much 
of  this  energy  corresponds  to  light  between  assigned  limits 
of  wave  length  we  must  express,  /  by  Fourier's  theorem,  in 
terms  of  an  harmonic  function  of  the  time. 

Let  us  take  the  following  case  as  representing  the 
stopping  and  starting  of  a  charged  particle  in  a  solid.  The 
particle  starts  from  rest,  for  a  time  ti  has  a  uniform 
acceleration  ft,  at  the  end  of  this  time  it  has  got  up  speed 
and  now  moves  for  a  time  £2  with  uniform  velocity,  at 
the  end  of  this  time  it  comes  into  collision,  and  we  suppose 
that  now  an  acceleration  —  ft  acts  for  a  time  ti  and  reduces 
it  to  rest  again, 

Thus  /when  expressed  as  a  function  of  the  time,  if  the 
time  t  =  o  is  taken  as  the  time  when  it  is  at  the  middle 
of  its  free  path,  has  the  following  values — 


f  =  o  from  t  =  —  oo  to  t  =  — 
f=P  from  t  =  -  (t,  +  |)  to  t  =  - 


/  =  o  from  t  =  —  £  to  t  =  -* 
A  '2 

/=  _  p  from  t  =  |  to  t  =  fi  + 

A 


J  =  o  from  t  =  ti  +      to  t  =  oo 

a 


92     THE    COKPUSCULAK   THEOEY   OF   MATTER. 

Now  by  Fourier's  theorem  we  have,  if  <t>  (t)  is  a  function 
off, 

4»  (t)  =  -   /""    f+  °°  <£  00  cos  q  (u  —  t)  dq  da 

7T    J  0       •*     -   oo 

applying  this  to  our  case,  and  performing  the  integrations, 
we  find 

IP  sing      sing  , 

/  =  -          /  2  %         9iu  q  t  .  d  g. 


7T 

0 


Now  Lord  Eayleigh  has  shown  (Philosophical  Magazine, 
June,  1889,  p.  466)  that  if 

<£(*)=-    f"  fi(q)8inqt.dq 

7T    J   0 


(t))*dt  =  i  /    (/i  (S))ad  g, 


hence — 

+"  ^"Ll    „    *1    0;M2/,    fo  +    ^ 


o 


d  q 


The  energy  radiated  from  the  charged  body  is  equal  to 

?  «-  /+>  At 
3  c    y-,/ 

32    e2 


hence  if  there  are  s  collisions  per  unit  volume  per  second 
the  energy  radiated  from  unit  volume  per  second  is 


*« 


dq, 


and   the   energy   corresponding   to   waves   which   have   a 
frequency  between  q  and  q  -}-  d  q  is  equal  to 


THEOKY  OF   ELECTEICAL   CONDUCTION.     93 

In  the  case  considered  by  Lorentz  the  waves  are  very 
long,  i.e.,  q  is  small  compared  with  l/h,  or  I/ft.  +  £2)  and 


n 


s  =     -  ;  in  this  case  the  preceding  expression  reduces  to 

A 


A        O   7T   C 

Now  j8  =  r/*i,  and  if  h,  i.e.,  the  time  occupied  by  the 
collisions  is  small  compared  with  t2  the  time  spent  in 
describing  the  free  path,  A  =  v  £2,  so  that  the  preceding 
expressions  become 

2   e*    \    2  7 
11  v          _  A  qL  d  q. 

o  TT  c 
Now  k,  the  electric  conductivity,  =  -:       —7-,    so    that  the 

4        at/ 

energy    radiated    from    unit    volume    in    unit    time    is 

8  a  0  7      o    7 
-  &  <?  dq. 

O    TT   C 

We  can  get  an  expression  for  the  stream  of  radiant 
energy  by  using  the  principle  that  when  things  have  got 
into  a  steady  state,  the  amount  of  energy  absorbed  by  unit 
volume  in  unit  time  is  equal  to  the  energy  radiated  from 
that  volume  in  the  same  time.  If  E  is  the  electric  force  in 
the  stream  of  radiant  energy  i  the  intensity  of  the  current, 
the  energy  absorbed  in  unit  volume  per  unit  time  is  E  i, 
or,  k  E2  since  i  =  k  E.  Now  W9  the  energy  per  unit 

K  E* 

volume,  is  equal  to  -      -  where  K  is  the  specific  inductive 

4     7T 

capacity  in  electromagnetic  units  ;  hence  the  rate  at  which 
energy  is  absorbed  is  —rr-  W,  and  this,  when  things  are 

in  a  steady  state,  must  be  equal  to  the  energy  radiated, 
hence  we  have 


94  THE  CORPUSCULAR  THEORY  OF  MATTER. 

the  energy  in  the  stream  of  radiant  energy  due  to  waves 
having  a  frequency  between  q  and  q  +  d  q  is  equal  to 

2  aOK    3  d 

If  /x  is  the  refractive  index  of  the  substance 

K  =  /*2/c2, 
hence  the  density  of  the  stream  of  radiant  energy  is 

2_.    /}       ^ 
a.(/     U  O        7 


fi  result  which  Lorentz  has  shown  agrees  well  with  the  actual 
determinations  of  the  radiation.  We  must  remember  that 
this  result  only  holds  when  the  frequency  of  the  waves  is 
very  small,  not  merely  because  it  is  only  in  this  case  that 
the  expression  A  reduces  to  B,  but  also  because  when  the 
frequency  is  large  the  conductivity  k  will  not  have  the 
value  we  have  assigned  to  it. 

To  return  to  the  expression  A  for  the  amount  of  energy 
radiated.  We  see  that  the  maximum  amount  of  the  energy 
for  a  given  difference  of  frequency  will  be  when  the  fre- 
quency is  such  that  qt\  is  small  and  q  (ti  +  t%)  finite,  i.e., 
when  the  time  of  vibration  of  the  light  is  comparable  with 
the  time  occupied  in  running  over  the  free  path : 
the  energy  in  the  light  with  this  frequency  is  greater 
than  in  the  light  whose  frequency  is  very  small ;  we  can, 
however,  easily  show  that,  as  we  should  expect,  the 
greatest  amount  of  energy  is  in  the  waves  whose  time  of 
vibration  is  comparable  with  t\9  the  time  occupied  by  a 
collision. 

We  can  see  this  as  follows; — since  the  rate  of  radiation  of 

2  e2  f* 

energy  is  -  -^~,   then    U  the  amount   radiated   by   one 
o     c 

corpuscle  in  the  case  we  have  considered  is — 


THEOEY  OF   ELECTEICAL   CONDUCTION.      95 

When  the  frequency  is  very  small,  the  energy  radiated 
having  a  frequency  between  q  and  q  -\-  d  q  is 


O  CTT 

or  Ui  the  total  energy  of  waves  having  frequencies  between 
o  and  q  is  given  by  the  equation 


as  both  qti  and  4  Ci  +  £2)  are  very  small,    C/i  is   only   a 
small  fraction  of   U,  the  total  amount  of  energy  radiated. 

Next  take  the  case  when  q  ti  is  very  small  and  q  (ti  +  tz) 
finite  ;  in  this  case  the  energy  between  q  and  q  +  d  q  is 

I*  P  *,&«&  +  ^dq, 

6  CTT  A 


and  C/2  the  value  of  this  over  a  range  q  is  given  by  the 
equation  — 

^2  =  \  -  ft2  *i  •  q  *i. 

6  CTT 

Since  q  ti  is  small,  we  see  that  U2  is  small  compared 
with  U  ;  it  is,  however,  large  compared  with  Ui,  the  long 
wave  thermal  radiation.  Since  Ui  and  f/2  are  each  small 
compared  with  U,  we  see  that  by  far  the  larger  part  of  the 
energy  will  be  in  the  light  whose  time  of  vibration  is  of 
the  same  order  as  the  time  occupied  by  a  collision.  If  this 
time  depends  on  the  temperature  diminishing  as  the 
temperature  increases,  and  if  at  a  certain  temperature  it  was 
of  the  same  order  as  the  time  of  vibration  of  visible  light, 
the  radiation  at  that  temperature  would  be  mainly  visible 
light  and  the  higher  the  temperature  the  bluer  the  light. 

The  assumptions  we  made  as  to  the  nature  of  the 
acceleration  of  the  charged  body,  that  it  was  equal  to  ft  for 
a  short  interval  ti,  then  equal  to  0  for  a  time  equal  to  /2, 
and  then  equal  to  —  ft  for  a  time  ti,  is  perhaps  more 
appropriate  to  the  first  theory  of  metallic  conduction  than 
to  the  second,  where  we  suppose  the  charged  body  pulled 
out  of  an  atom  by  the  attraction  of  B,  and  being  suddenly 


96  THE  COKPUSCULAR  THEORY  OF  MATTER. 

stopped  when  it  strikes  against  B.  For  this  case  it  is  more 
appropriate  to  suppose  that  /  is  equal  to  ft  for  a  time  t2, 
and  then  equal  to  —  ft  for  a  very  short  time  ti,  where 
ft  t2  =  ft  fi. 

By  applying  the  same  method  as  before  we  can  easily 
show  that  the  energy  of  light  with  frequency  between  q  and 
q  +  d  q  radiated  in  unit  time  from  unit  volume  is  — 

2     £2     (  r>  »       •    o  Ql  U  no      •     o 


or 


»       •    o     l  n 

5—  -    »  sm  -TV  +  A.  sin 

3  TT  c  V  2  2 

-  2  ft  ft  «iw  ll2  sin  *£  cos  q  (t,  +  t2)]  ^, 
^  ^  ^ 


r 

2J?  \ 

2    cos  q  (h  +  f2)    }  d  q. 


For  very  small  values  of  q  this  reduces  to 
s\^-c^t^(h  +  t^(fdq; 
or,  since  ti  is  small  compared  with  t2, 


Now  J  ft  t22  is  the  space  passed  over  by  the  charged 
body  while  its  motion  is  being  accelerated  ;  it  is,  therefore, 
equal  to  b,  the  distance  separating  the  systems  between 
which  the  charged  body  travels,  hence  the  energy  radiated 
from  unit  volume  per  second  is  — 

2  s  e2  72    o  , 
3.-6  q  dq- 

If  W  is  the  stream  of  radiant  energy  between  these 
limits  of  frequency  flowing  through  the  body  we  have  as 
before 

4  TT  A:  c2  2  s  e2 


THEOKY  OF   ELECTEICAL   CONDUCTION.     97 

where  k  is  the  electrical  conductivity,  and  on  this  theory 

_  2 
= 


_  2  e*Pnl)d 


Now  s  =  n  fj?,  hence 

TT7      3  a  6  p  b    o7 

vlibV**' 

while  on  the  other  theory  it  was  (see  page  94)  given  by 
the  equation  — 


If,  as  we  should  expect  in  a  good  conductor,  b  is  very 
nearly  equal  to  d,  the  radiation  on  the  new  theory  is  to 
that  on  the  old  as  9  to  8.  Thus  the  expressions  are  so 
nearly  equal  that  in  the  present  state  of  our  knowledge  we 
cannot  say  that  in  this  respect  the  one  theory  agrees  better 
with  the  facts  than  the  other. 

On  this  theory  by  far  the  greater  part  of  the  radiation 
which  starts  from  the  metal  is  of  exceedingly  short  wave 
length,  the  time  of  vibration  being  comparable  with  t\. 

PELTIER  AND  THOMSON  EFFECTS. 

These  effects  on  the  theory  first  discussed,  that  corpuscles 
are  distributed  throughout  the  metal  and  are  in  temperature 
equilibrium  with  it,  may  be  regarded  as  arising  in  the 
following  way.  If  there  are  n  corpuscles  per  unit  volume 
and  v  is  their  average  velocity,  then  through  unit  area  in 
the  metal,  J  n  v  corpuscles  will  in  one  second  pass  through  in 
one  direction.  Hence  if  we  have  two  metals  A  and  B  in 
contact,  and  if  n  v  in  A  is  not  the  same  as  in  B,  the  number 
of  corpuscles  that  flow  from  A  to  B  will  not  be  the  same  as 
the  number  that  flow  from  B  to  A.  To  fix  our  ideas,  let  us 
suppose  that  the  flow  through  A  is  greater  than  that 
through  B  ;  A  will  lose  more  corpuscles  than  it  will  gain 
and  so  will  become  positively,  while  B  will  be  negatively, 
electrified.  This  distribution  of  electricity  will  tend  to 
dimmish  the  flow  of  corpuscles  from  A  and  increase  that 

T.M.  H 


98  THE  COEPUSCULAK  THEORY  OF  MATTER. 

from  B,  and  the  charges  of  electricity  will  accumulate  until 
they  have  made  the  two  flows  equal,  when  things  will  be  in 
a  steady  state.  This  accumulation  of  positive  electricity 
on  A  and  of  negative  on  B  will  form  an  "  electric  double 
layer  "  between  the  coatings  of  which  there  is  a  finite  poten- 
tial difference  which  is  a  measure  of  the  Peltier  effect  at  the 
junction  of  the  metals.  Similarly,  if  the  flow  J  n  v  depends 
upon  the  temperature  of  the  metal,  the  transport  of 
corpuscles  through  each  section  of  an  unequally  heated 
conductor  will  vary,  and  the  state  of  the  conductor  cannot 
be  steady  :  the  difference  in  the  amount  flowing  through 
different  sections  will  produce  an  accumulation  of  electricity 
along  the  conductor  ;  this  will  produce  an  electric  force 
which,  by  increasing  the  flow  where  it  was  small  and 
diminishing  it  where  it  was  large,  will  make  the  flow  uniform 
throughout  the  conductor.  These  forces  represent  the 
Thomson  effect. 

In  the  second  theory,  where  the  corpuscles  are  supposed 
to  start  from  one  electric  doublet  and  come  to  rest  on 
another,  there  is  a  movement  of  corpuscles  throughout  the 
body,  and  we  easily  see  that,  with  the  notation  of  page  88, 
the  number  of  corpuscles  which  pass  in  one  second,  in  one 
direction  through  unit  area,  is 


Hence,  as  before,  if  two  metals  A  arid  B  are  in  contact  and 
if  n  p  b  for  A  is  not  the  same  as  for  B,  one  metal  will  gain 
and  the  other  lose  electricity:  thus  there  will  be  an  accumu- 
lation of  electricity  at  the  junction  producing  an  electric 
field;  this  field  will  increase  the  flow  in  one  metal  and 
retard  it  in  the  other  until  the  two  flows  are  equal. 

The  manner  in  which  the  electric  force  affects  the  flow  of 
the  corpuscles  is  essentially  different  in  the  two  theories. 
On  the  first  theory  the  electric  force  acts  on  the  free 
corpuscles,  accelerating  those  in  one  metal  and  retarding 
those  in  the  other,  while  on  the  second  theory  the  alteration 
in  the  flow  is  brought  about  by  the  action  of  the  electric 


THEORY  OF   ELECTRICAL   CONDUCTION.      99 

field  on  the  doublets  which  are  supposed  to  be  dispersed 
through  the  metal  and  not  on  the  free  corpuscles.  If  the 
axes  of  these  doublets  are  distributed  uniformly  in  all 
directions,  then  the  flow  of  corpuscles  produced  by  the  detach- 
ment of  corpuscles  from  the  doublets  will  be  uniform  in  all 
directions.  If,  however,  an  electric  force  which  we  may 
suppose  to  be  parallel  to  the  axis  of  x  acts  on  the  metal,  it 
will  polarise  the  distribution  of  the  axes  of  the  doublets 
and  will  make  more  point  in  the  direction  of  the  axis  of  x 
than  in  the  opposite  direction ;  thus  this  electric  force  will 
diminish  the  flow  of  corpuscles  along  the  positive  direction 
of  x  while  it  will  increase  the  flow  in  the  opposite  direction. 
We  see  that  by  the  application  of  suitable  electric  forces  we 
can  increase  or  diminish  the  flow  in  any  direction.  At  the 
junction  of  two  metals  the  initial  inequality  in  the  flow  of 
corpuscles  across  the  junction  will  cause  an  accumulation 
of  electricity,  and  this  will  go  on  until  the  forces  due  to  this 
electrification  have  made  the  flows  in  the  two  metals  equal 
to  each  other ;  it  is  these  forces  which  give  rise  to  the 
Peltier  effect,  while  the  Thomson  effect  is  represented  by 
the  forces  which  are  required  to  make  the  flow  of  cor- 
puscles uniform  at  all  points  in  an  unequally  heated 
conductor. 

ON  THE  HALL  EFFECT  AND  THE  EFFECT  OF  A  MAGNETIC 
FIELD  ON  ELECTRICAL  RESISTANCE. 

The  Hall  effect,  on  the  second  theory  of  metallic  con- 
duction, originates  in  the  action  of  the  magnetic  field  on 
the  distribution  of  the  axes  of  the  doublet  which  .are 
supposed  to  exist  in  the  metal,  while  on  the  first  theory 
it  arose  from  the  action  of  the  magnetic  field  on  the 
corpuscles. 

To  see  how  it  arises  on  the  second  theory,  let  us  suppose 
that  AB  is  a  doublet  and  that  an  electric  force  parallel  to  the 
axis  of  x  acts  upon  it ;  this  electric  field  will  give  rise  to  a 
couple  tending  to  bring  the  axis  of  the  doublet  in  line  with  the 
force.  If  the  motion  of  the  doublet  takes  place  in  a  magnetic 

H  2 


100  THE  CORPUSCULAR  THEOKY  OF  MATTER. 

field,  then  as  soon  as  the  doublet  begins  to  move  the  mov- 
ing positive  and  negative  charges  at  its  ends  will  be  acted 
upon  by  forces  which  are  at  right  angles  to  the  magnetic 
force  and  at  right  angles  also  to  the  direction  of  motion  of 
the  charges.  If  the  doublet  were  turning  about  a  point  mid- 
way between  the  charges,  the  velocity  of  the  negative 
charge  would  be  equal  and  opposite  to  that  of  the  positive,  so 
that  the  same  force  would  be  exerted  by  the  magnetic  field  on 
the  two  charges,  and  the  joint  effect  of  the  two  forces  on  the 
doublet  would  be  to  pull  it  bodily  in  some  direction  without 
deflecting  the  axis ;  in  this  case  there  would  not  be  any 
Hall  effect.  Suppose,  however,  that  the  doublet  were  not 
turning  about  the  point  midway  between  the  charges,  so 


FIG.  23. 

that  the  velocities  of  these  charges  were  not  equal  and 
opposite,  then  the  force  due  to  the  magnetic  field  on  the 
one  would  not  be  equal  to  that  on  the  other  ;  the  forces 
would  have  a  finite  moment  about  an  axis  through  the 
point  about  which  the  doublet  is  turning,  and  there  would 
be  a  couple  tending  to  deflect  the  axis  of  the  doublet.  If  the 
couples  arising  in  this  way  all  tended  to  twist  the  axes  of 
the  doublets  in  one  direction,  there  would  be  an  excess  of 
the  axes  pointing  in  this  direction  over  those  pointing  in 
the  opposite,  and  therefore  a  current  in  that  direction ;  thus 
the  magnetic  force  might  give  rise  to  side  currents 
analogous  to  those  which  constitute  the  Hall  effect. 

To  follow  this  effect  into  greater  detail,  let  us  consider 
what  will  happen  when  the  point  about  which  the  doublet 


THEOEY  OF   ELECTEICAL   CONDUCTION.     101 

AB  turns  coincides  with  one  of  the  charges,  say,  the 
negative  charge  A ;  let  the  magnetic  force  act  in  the 
direction  OY,  the  electric  force  along  OX  (Fig.  23).  Con- 
sider a  doublet  AB  originally  in  the  plane  XOY,  then,  under 
the  action  of  the  electric  force,  AB  will  begin  to  approach 
OX,  but  as  the  positive  charge  moves  in  the  magnetic  field 
it  will  be  acted  on  by  a  downward  force,  making  B  dip 
below  the  plane  XOY,  and  thus  making  the  negative  end  of 
the  doublet  be  above  the  positive  end.  This  would  have 
the  effect  of  making  more  doublets  have  their  negative  ends 
above  the  positive  than  below  it;  there  would  thus  be  a 
vertically  downward  current  of  electricity,  i.e.,  a  current  at 
right  angles  to  both  the  magnetic  and  electric  forces,  i.e., 
a  current  in  the  direction  of  the  Hall  effect.  If  the  positive 
end  of  the  doublet  had  been  fixed  instead  of  the  negative 
end,  the  couple  tending  to  twist  the  axis  of  the  doublet  would 
be  reversed,  and  there  would  be  a  majority  of  doublets 
having  their  positive  ends  above  the  negative,  i.e.,  there 
would  be  a  current  of  electricity  vertically  upwards  instead 
of  downwards.  This  would  correspond  to  a  Hall  effect  of 
the  opposite  sign  to  the  preceding.  The  sign  of  the  Hall 
effect  would  depend  upon  whether  the  positive  or  the 
negative  end" of  the  doublet  moves  the  faster  when  the 
doublet  is  deflected  by  the  electric  force.  The  bias  which 
the  axis  of  the  doublet  experiences  in  consequence  of  the 
magnetic  force  makes  the  average  angle  made  by  the  axis 
of  the  doublet  with  the  direction  of  the  electric  force 
greater  than  it  would  be  if  the  magnetic  force  were  absent, 
just  as  the  average  angle  made  with  the  vertical  by  a 
pendulum  having  for  a  bob  a  gyroscope  in  rapid  rotation 
is  greater  than  that  for  the  pendulum  started  from  the 
same  position  with  the  bob  at  rest.  This  increase  in  the 
angle  between  the  direction  of  the  electric  force  and  the 
axes  of  the  doublets  means  that  the  polarisation  and 
therefore  the  electric  current  is  less  than  it  would  be  if  the 
magnetic  force  were  absent,  or,  as  we  may  express  it,  the 
resistance  of  the  conductor  is  increased  by  the  magnetic 
force. 


10'2     THE    COKPUSCULAB   THEOEY  OF   MATTER 

It  will  be  noticed  that  the  expressions  we  have  found  for 
the  electrical  and  thermal  conductivities,  the  radiation,  and 
the  other  electrical  effects  do  not  involve  the  mass  of  the 
carrier,  so  that  the  results  would  hold  if  the  carriers  were 
bodies  having  a  much  greater  mass  than  that  of  a 
corpuscle. 


CHAPTEE  YL 

THE  ARRANGEMENT  OF  CORPUSCLES  IN  THE  ATOM. 

WE  have  seen  that  corpuscles  are  always  of  the  same 
kind  whatever  may  he  the  nature  of  the  substance  from 
which  they  originate  ;  this,  in  conjunction  with  the  fact 
that  their  mass  is  much  smaller  than  that  of  any  known 
atom,  suggests  that  they  are  a  constituent  of  all  atoms;  that, 
in  short,  corpuscles  are  an  essential  part  of  the  structure  of 
the  atoms  of  the  different  elements.  This  consideration 
makes  it  important  to  consider  the  ways  in  which  groups  of 
corpuscles  can  arrange  themselves  so  as  to  be  in  equilibrium. 
Since  the  corpuscles  are  all  negatively  electrified,  they  repel 
each  other,  and  thus,  unless  there  is  some  force  tending  to 
hold  them  together,  no  group  in  which  the  distances  between 
the  corpuscles  is  finite  can  be  in  equilibrium.  As  the  atoms  of 
the  elements  in  their  normal  states  are  electrically  neutral, 
the  negative  electricity  on  the  corpuscles  they  contain  must 
be  balanced  by  an  equivalent  amount  of  positive  electricity; 
the  atoms  must,  along  with  the  corpuscles,  contain  positive 
electricity.  The  form  in  which  this  positive  electricity 
occurs  in  the  atom  is  at  present  a  matter  about  which  we 
have  very  little  information.  No  positively  electrified  body 
has  yet  been  found  having  a  mass  less  than  that  of  an  atom 
of  hydrogen.  All  the  positively  electrified  systems  in  gases 
at  low  pressures  seem  to  be  atoms  which,  neutral  in  their 
normal  state,  have  become  positively  charged  by  losing  a 
corpuscle.  In  default  of  exact  knowledge  of  the  nature  of 
the  way  in  which  positive  electricity  occurs  in  the  atom,  we 
shall  consider  a  case  in  which  the  positive  electricity  is  dis- 
tributed in  the  way  most  amenable  to  mathematical  calcula- 
tion, i.e.,  when  it  occurs  as  a  sphere  of  uniform  density, 
throughout  which  the  corpuscles  are  distributed.  The  positive 


104  THE  CORPUSCULAR  THEORY  OF  MATTER. 

electricity  attracts  the  corpuscles  to  the  centre  of  the  sphere, 
while  their  mutual  repulsion  drives  them  away  from  it ; 
when  in  equilibrium  they  will  be  distributed  in  such  a 
way  that  the  attraction  of  the  positive  electrification  is 
balanced  by  the  repulsion  of  the  other  corpuscles. 

Let  us  now  consider  the  problem  as  to  how  1...2...3...  n 
corpuscles  would  arrange  themselves  if  placed  in  a  sphere 
filled  with  positive  electricity  of  uniform  density,  the  total 
negative  charge  on  the  corpuscles  being  equivalent  to  the 
positive  charge  in  the  sphere. 

When  there  is  only  one  corpuscle  the  solution  is  very 
simple :  the  corpuscle  will  evidently  go  to  the  centre  of  the 
sphere.  The  potential  energy  possessed  by  the  different 
arrangements  is  a  quantity  of  considerable  importance  in 
the  theory  of  the  subject.  We  shall  call  Q  the  amount  of 
work  required  to  remove  each  portion  of  electricity  to  an 
infinite  distance  from  its  nearest  neighbour  ;  thus  in  the  case 
of  the  single  corpuscle  we  should  have  to  do  work  to  drag 
the  corpuscle  out  of  the  sphere  and  then  carry  it  away  to 
an  infinite  distance  from  it ;  when  we  have  done  this  we 
should  be  left  with  the  sphere  of  positive  electricity,  the 
various  parts  of  which  would  repel  each  other ;  if  we  let 
these  parts  recede  from  each  other  until  they  were  infinitely 
remote  we  should  gain  work.  The  difference  between  the 
work  spent  in  removing  the  negative  from  the  positive  and 
that  gained  by  allowing  the  positive  to  scatter  is  Q  the 
amount  of  work  required  to  separate  completely  the 
electrical  charges.  When  there  is  only  one  corpuscle  we 

9    e2 

can  easily  show  that  Q  =  —  — ,  where  e  is  the  charge  on  a 

J.U  a 

corpuscle  measured  in  electrostatic  units  and  a  is  the  radius 
of  the  sphere. 

When  there  are  two  corpuscles  inside  a  sphere  of  positive 
electricity  they  will,  when  in  equilibrium,  be  situated  at 
two  points  A  and  B,  in  a  straight  line  with  0  the  centre  of 

the  sphere  and  such  that  OA  =  OB=^,  where  a  is  the 
radius  of  the  sphere.  We  can  easily  show  that  in  this  position 


ARRANGEMENT   OF    CORPUSCLES   IN   ATOM.     105 

the  repulsion  between  A  and  B  is  just  balanced  by  the 
attraction  of  the  positive  electricity  and  also  that  the 
equilibrium  is  stable.  We  may  point  out  that  A  B  the 
distance  between  the  corpuscles  is  equal  to  the  radius  of 
the  sphere  of  positive  electrification.  In  this  case  we  can 

21  e2 
show  that  Q  —  ^ — . 

J-U     Ci 

Thus  if  the  radius  of  the  sphere  of  positive  electrification 
remained  constant,  Q  for  a  system  containing  two  corpuscles 
in  a  single  sphere  would  be  greater  than  Q  for  the  arrange- 
ment in  which  each  corpuscle  is  placed  in  a  sphere  of 
positive  electrification  of  its  own,  for  in  the  latter  case  we 

9   <r  21  e2 

have  seen  that  Q  =  2  X  ^  ~  and  this  is  less  than  T    — . 

10  a  1U  a 

Thus  the  arrangement  with  the  two  corpuscles  inside  one 
sphere  is  more  stable  than  that  where  there  are  two  spheres 
with  a  single  corpuscle  inside  each  :  thus  if  we  had  a  number 
of  single  corpuscles  each  inside  its  own  sphere,  they  would 
not  be  so  stable  as  if  they  were  to  coagulate  and  form  systems 
each  containing  more  than  one  corpuscle.  There  would  there- 
fore be  a  tendency  for  a  large  number  of  systems  containing 
single  corpuscles  to  form  more  complex  systems.  This  result 
depends  upon  the  assumption  that  the  size  of  the  sphere  of 
positive  electrification  for  the  system  containing  two  cor- 
puscles is  the  same  as  that  of  the  sphere  containing  only 
one  corpuscle.  If  we  had  assumed  that  when  two  systems 
unite  the  volume  of  the  sphere  of  positive  electricity  for 
the  combined  system  is  the  sum  of  the  volumes  of  the 
individual  systems,  then  a  for  the  combined  system  would 
be  2J  or  1*25  times  a  for  the  single  system.  Taking  this 
into  account,  we  find  that  Q  for  the  combined  system  is 
less  than  the  sum  of  the  values  of  Q  for  the  individual 
system ;  in  this  case  the  system  containing  two  corpuscles 
would  not  be  so  stable  as  two  systems  each  containing  one 
corpuscle,  so  that  the  tendency  now  would  be  towards 
dissociation  rather  than  association. 

Three  corpuscles  inside  a  single  sphere  will  be  in  stable 
equilibrium  when  at  the  corners  of  an  equilateral  triangle 


106     THE    CORPUSCULAR   THEORY   OF   MATTER. 

whose  centre  is  at  the  centre  of  the  sphere  and  whose  side  is 
equal  in  length  to  the  radius  of  that  sphere;  thus  for  three  as 
for  two  corpuscles  the  equilibrium  position  is  determined  by 
the  condition  that  the  distance  between  two  corpuscles  is 
equal  to  the  radius  of  the  sphere  of  positive  electrification. 

For  the  case  of  three  corpuscles  Q  =  -    — ,    and  thus 

JLU  a 

again  we  see  that  if  the  radius  of  the  sphere  of  positive 
electricity  is  invariable,  the  arrangement  with  three  cor- 
puscles inside  one  sphere  is  more  stable  than  three  single 
corpuscles  each  inside  its  own  sphere,  or  than  one  corpuscle 
inside  one  sphere  and  two  corpuscles  inside  another  sphere  ; 
thus  again  the  tendency  would  be  towards  aggregation.  If, 
however,  the  positive  electricity  instead  of  being  invariable 
in  size  were  invariable  in  density,  we  see  that  the  tendency 
would  be  for  the  complex  system  to  dissociate  into  the 
simpler  ones. 

Four  corpuscles  if  at  rest  cannot  be  in  equilibrium  when 
in  one  plane,  although  the  co-planar  arrangement  is  possible 
and  stable  when  the  four  are  in  rapid  rotation.  When  there 
is  no  rotation  the  corpuscles,  when  in  stable  equilibrium,  are 
arranged  at  the  corners  of  a  regular  tetrahedron  whose 
centre  is  at  the  centre  of  the  sphere  of  positive  electrifica- 
tion and  whose  side  is  equal  to  the  radius  of  that  sphere ; 
thus  we  again  have  the  result  that  the  distance  between  the 
corpuscles  is  equal  to  the  radius  of  the  positive  sphere. 

2    K.  A 

For  four  corpuscles  Q  =  —]£.  We  see  that  the  values  of 

a  10 

Q  per  corpuscle  are  for  the  arrangements  of  1,  2,  3,  4  cor- 
puscles in  the  proportion  of  6  :  7  :  8  :  9  if  the  radius  of  the 
positive  sphere  is  invariable. 

Six  corpuscles  will  be  in  stable  equilibrium  at  the  corners 
of  a  regular  octahedron,  but  it  can  be  shown  that  the  equi- 
librium of  eight  corpuscles  at  the  corners  of  a  cube  is 
unstable.  The  general  problem  of  finding  how  n  corpuscles 
will  distribute  themselves  inside  the  sphere  is  very  com- 
plicated, and  I  have  not  succeeded  in  solving  it ;  we  can, 
however,  solve  the  special  case  where  the  corpuscles  are 


ARKANGEMENT   OF    COKPUSCLES   IN   ATOM.     107 

confined  to  a  plane  passing  through  the  centre  of  the 
sphere,  and  from  the  results  obtained  from  this  solution  we 
may  infer  some  of  the  properties  of  the  more  general 
distribution.  The  analytical  solution  of  the  problem  when 
the  motion  of  the  corpuscles  is  confined  to  one  plane  is 
given  in  a  paper  by  the  author  in  the  Philosophical  Magazine 
for  March,  1904 ;  we  shall  refer  to  that  paper  for  the 
analysis  and  quote  here  only  the  results. 

If  we  have  n  corpuscles  arranged  at  the  corners  of  a 
regular  polygon  with  n  sides  with  its  centre  at  the  centre  of 
the  sphere  of  positive  electrification,  each  corpuscle  being 
thus  at  the  same  distance  r  from  the  centre  of  this  sphere, 
we  can  find  a  value  of  r,  so  that  the  repulsion  exerted  by 
the  (n  —  1)  corpuscles  on  the  remaining  corpuscle  is  equal  to 
the  attraction  of  the  positive  electricity  on  that  corpuscle  ; 
the  ring  of  corpuscles  would  then  be  in  equilibrium.  But  it 
is  shown  in  the  paper  referred  to  that  if  n  is  greater  than  5 
the  equilibrium  is  unstable  and  so  cannot  exist ;  thus  5  is 
the  greatest  number  of  corpuscles  which  can  be  in  equili- 
brium as  a  single  ring.  It  is  shown,  however,  that  we 
can  have  a  ring  containing  more  than  five  corpuscles  in 
equilibrium  if  there  are  other  corpuscles  inside  the  ring. 
Thus,  though  a  ring  of  six  corpuscles  at  the  corners 
of  a  regular  hexagon  is  unstable  by  itself,  it  becomes 
stable  when  there  is  another  corpuscle  placed  at  the 
centre  of  the  hexagon,  and  rings  of  seven  and  eight 
corpuscles  are  also  made  stable  by  placing  one  corpuscle 
inside  them.  To  make  a  ring  of  nine  corpuscles  stable, 
however,  we  must  have  two  corpuscles  inside  it,  and 
the  number  of  corpuscles  required  inside  a  ring  to  keep  it 
stable  increases  very  rapidly  with  the  number  of  corpuscles 
in  the  ring.  This  is  shown  by  the  following  Table,  where  n 
represents  the  number  of  corpuscles  in  the  ring  and  i  the 
number  of  corpuscles  which  must  be  placed  inside  the  ring 
to  keep  it  in  stable  equilibrium  :— 

n.  5.  6.  7.  8.  9.  10.  12.  13.  15.  20.  30.  40. 
i.  0.  1.  1.  1.  2.  3.  8  10.  15.  39.  101.  232. 


108    THE   COBPUSCULAR   THEOEY  OF   MATTEK. 

When  n  is  large  i  is  proportional  to  n3.  We  thus  see 
that  in  the  case  when  the  corpuscles  are  confined  to  one 
plane  they  will  arrange  themselves  in  a  series  of  concentric 
rings.  When  we  have  determined  the  relation  between  n  and 
?',  i.e.,  have  found  that  i  =  f  (n}  where  /  is  a  known  func- 
tion, the  problem  of  finding  the  configuration  of  N  corpuscles 
when  in  stable  equilibrium  admits  of  a  very  simple  solution. 
When  the  number  of  rings  is  as  small  as  possible  the 
number  of  corpuscles  in  each  ring  will  be  as  large  as 
possible.  If  H!  is  the  number  in  the  outer  ring  then  there 
will  be  N  —  n-i  inside  it,  and  if  these  are  just  sufficient  to 
keep  the  outer  ring  in  stable  equilibrium  N  —  m  =  f  (n^), 


100 


FIG.    24. 


the  solution  of  this  equation  will  give  us  nlt     To  find  ?/2,  the 
number  in  the  next  ring,  we  evidently  have  the  equation — 

N  —  ?li  —  77  2  =/(tta), 

while   7i3,  the  number  in  the   next   ring,  is   given   by  the 
equation — 

N  —  Wj  —  Wa=/(w3), 

and  so  on. 

These  equations  can  be  solved  very  rapidly  by  a  graphical 
method.  Draw  the  graph  whose  abscissa  =f(n)  and  whose 
ordinate  is  n;  the  values  of/  (n)  for  a  series  of  values  of  n 
are  given  on  page  107;  from  these  values  the  curve  (Fig.  24) 
has  been  constructed. 

To  find  how  a  number  of  corpuscles  equal  to  N  will 
arrange  themselves,  measure  off  along  the  axis  of  abscissae 
a  distance  from  0  equal  to  N.  Let  O  P  be  this  distance ; 
through  P  draw  the  straight  line  P  Q  inclined  at  an  angle 


AEEANGEMENT   OF   CORPUSCLES   IN   ATOM.     109 

of  135°  to  the  horizontal  axis,  intersecting  the  curve  in  Q, 
draw  the  ordinate  Q  M,  then  the  integral  part  of  Q  M  will 
be  the  value  of  nit  the  number  of  corpuscles  in  the  outside 
ring.  For  evidently 

OM=f(QM) 

and  0  M  =  0  P  —  P  M,  and  since  P  Q  is  inclined  at  45° 
to  the  axis,  Q  M  =  P  M ,-  hence 

OP-QM=f(QM). 

comparing  this  with  the  equation  N  —  HI  =  f  (HI),  we  see 
that  the  integral  part  of  Q  M  is  equal  to  nr 

To  get  the  value  of  nz,  the  number  of  the  corpuscles  in 
the  second  ring,  we  mark  off  the  abscissa  0  P1  =  N  —  HI ; 
if  Q  M  is  an  integer  Pl  will  coincide  with  M ;  from  Px 
draw  Pl  Q!  parallel  to  P  Q,  cutting  the  curve  in  Q^ ;  if  Ql  MI 
is  the  ordinate  at  Q19  the  integral  part  of  Q±  MI  will  be  the 
value  of  nz.  To  get  n3  mark  off  0  P2  =  N  —  HI  —  «2  and 
draw  P2  Q2  parallel  to  P  Q ;  the  integral  part  of  Q2  M2  will  be 
the  value  n3.  In  this  way  we  can,  in  a  very  short  time,  find 
the  numbers  of  corpuscles  in  the  various  rings. 

The  following  Table  giving  the  various  rings  for  corpuscles 
ranging  in  number  from  1  to  100  has  been  calculated  in  this 
way ;  the  first  row  contains  the  numbers  for  which  there  is 
only  one  ring,  the  second  those  with  two  rings,  the  third 
those  with  three,  and  so  on : — 

NUMBERS  OP  CORPUSCLES  IN  ORDER. 
12345 

5     6     7     8     8     8    ^  10  10  10  11 
11112333455 

11  11  11  12  12  12  13  13  13  13  13  14  14  15  15 
5  6  7  7  8  8  8  8  9  10  10  10  10  10  11 
111112333344555 

15  15  15  16  10  16  16  16  16  16  17  17  17  17  17  17  17 
11  11  11  11  12  12  12  13  13  13  13  13  13  14  14  15  15 

5  6  7  7  7  8  8  8  8  9  9  10  10  10  10  10  11 

11111122333344555 

17  18  18  18  18  18  19  19  19  19  20  20  20  20  20  20  20  20  20  21  21 

15  15  15  15  16  16  16  16  16  16  16  16  16  17  17  17  17  17  17  17  17 

11  11   11  11  1112  12  12  12  13  13  13  13  13  13  13  14  14  15  15  15 

5     5     6     7     7     7     7     8     8     8     8     8     9     9  10  10  10  10  10  10  11 

111111112223333445555 


110  THE  CORPUSCULAR  THEORY  OF  MATTER. 

NUMBER  OF  CORPUSCLES  IN  ORDER — continued. 

21   21   21   21   21  21   21  21  22  22  22  22  22  22  22  22  23  23  23  23  23  23  23  24 

17  18  18  18  18  18  19  19  19  19  19  20  20  20  20  20  20  20  20  20  20  21  21  21 

15  15  15  15  16  1(5  lf>  16  16  16  16  16  16  16  17  17  17  17  17  17  17  17  17  17 

11  11  11  11  11  12  12  12  12  12  13  13  13  13  13  13  13  13  14  14  15  15  15  15 

5     5     6     7     7     7     7     8     8     8     8     8     8     9     9  10  10  10  10  10  10  10  11  11 

111111111222333334455555 

24  24  24  24  24  24  24 
21  21  21  21  21  21  21 
17  18  18  18  18  18  19 
15  15  15  15  16  16  16 
11  11  11  11  11  12  12 

5567777 

1111111 

We  can  investigate  the  equilibrium  of  corpuscles  in  one 
plane  by  experiment  as  well  as  by  analysis,  using  a 
method  introduced  for  a  different  purpose  by  an  American 
physicist,  Professor  Mayer.  The  problem  of  the  arrange- 
ment of  the  corpuscles  is  to  find  how  a  number  of  bodies 
which  repel  each  other  with  forces  inversely  proportional  to 
the  square  of  the  distance  between  them  will  arrange  them- 
selves when  under  the  action  of  an  attractive  force  tending 
to  drag  them  to  a  fixed  point.  For  the  experimental  method 
the  corpuscles  are  replaced  by  magnetised  needles  pushed 
through  cork  discs  and  floating  on  water.  Care  should  be 
taken  that  the  needles  are  equally  magnetised.  These 
needles,  having  their  poles  all  pointing  in  the  same  way, 
repel  each  other  like  the  corpuscles.  The  attractive  force  is 
produced  by  a  large  magnet  placed  above  the  surface  of  the 
water,  the  lower  pole  of  this  magnet  being  of  the  opposite 
sign  to  that  of  the  upper  poles  of  the  floating  magnets.  The 
component  along  the  surface  of  the  water  of  the  force  due 
to  this  magnet  is  directed  to  the  point  on  the  surface 
vertically  below  the  pole  of  the  magnet,  and  is  approximately 
proportional  to  the  distance  from  this  point.  The  forces 
acting  on  the  magnets  are  thus  analogous  to  those  acting  on 
the  corpuscles. 

If  we  throw  needle  after  needle  into  the  water  we  shall 
find  that  they  will  arrange  themselves  in  definite  patterns, 
three  needles  at  the  corners  of  a  triangle,  four  at  the  corners 
of  a  square,  five  at  the  corners  of  a  pentagon;  when,  however, 


ARRANGEMENT   OF   CORPUSCLES   IN   ATOM.     Ill 

we  throw  in  a  sixth  needle  this  sequence  is  broken  ;  the  six 
needles  do  not  arrange  themselves  at  the  corners  of  a  hexagon, 
but  five  go  to  the  corners  of  a  pentagon  and  one  goes  to 
the  middle.  When  we  throw  in  a  seventh  needle  we  get  a 
ring  of  six  with  one  at  the  centre  ;  thus  a  ring  of  six,  though 
unstable  when  hollow,  becomes  stable  as  soon  as  one 
is  put  in  the  inside.  This  is  an  example  of  a  fundamental 
principle  in  the  stable  configurations  of  corpuscles;  the 


FIG.  25. 

structure  must  be  substantial;  we  cannot  have  a  great 
display  of  corpuscles  on  the  outside  and  nothing  in  the 
inside.  If,  however,  we  have  a  good  foundation  of  cor- 
puscles— if,  for  example,  we  tie  a  considerable  number  of 
needles  together  for  the  inside — we  can  have  a  ring  containing 
a  large  number  of  corpuscles  in  stable  equilibrium  around 
it,  although  five  is  the  greatest  number  of  corpuscles  that 
can  be  in  equilibrium  in  a  hollow  ring.  By  the  aid  of  these 
floating  magnets  we  can  illustrate  the  configurations  for 


112  THE  CORPUSCULAR  THEORY  OF  MATTER. 

considerable  numbers  of  corpuscles,  and  verify  the  Table 
previously  given. 

Another  method,  due  to  Professor  R.  W.  Wood,  is  to 
replace  the  magnets  floating  on  water  by  iron  spheres 
floating  on  mercury ;  these  spheres  get  magnetised  by 
induction  by  the  large  magnet  placed  above  them  and  repel 
each  other — though  in  this  case  the  repulsive  force  does  not 
vary  inversely  as  the  square  of  the  distance — while  they  are 
attracted  by  the  external  magnet ;  the  iron  spheres  arrange 
themselves  in  patterns  analogous  to  those  formed  by  the 
magnets.  Dr.  Monckman  used,  instead  of  magnets, 
elongated  conductors  floating  vertically  in  water ;  these  were 
electrified  by  induction  by  a  charged  body  held  above  the 
surface  of  the  water;  the  conductors,  being  similarly 
electrified,  repelled  each  other  and  were  attracted  towards 
the  electrified  body ;  under  these  forces  they  formed  patterns 
similar  to  those  formed  by  the  floating  magnets. 

We  see  from  this  experimental  illustration,  as  well  as  by 
the  analytical  investigation,  that  a  number  of  corpuscles 
will,  if  confined  to  one  plane,  arrange  themselves  in  a  series 
of  rings,  the  number  of  corpuscles  in  the  ring  increasing  as 
the  radius  of  the  ring  increases. 

If  we  refer  to  the  arrangements  of  the  different  numbers  of 
corpuscles  given  on  page  109,  we  see  that  the  numbers  which 
come  in  the  same  vertical  columns  are  arranged  in  patterns 
which  have  much  in  common,  for  each  arrangement  is 
obtained  by  adding  another  storey  to  the  one  above  it. 
Thus,  to  take  the  first  column,  we  have  the  pattern  5,  1, 
the  one  below  it  is  11,  5,  1 ;  the  one  below  this  15,  11,  5,  1; 
the  one  below  this  17, 15, 11,  5, 1;  then  21,  17, 15, 11,  5, 1; 
and  then  24,  21,  17,  15,  11,  5,  1.  We  should  expect  the 
properties  of  the  atoms  formed  of  such  arrangements  of 
corpuscles  to  have  many  points  of  resemblance.  Take,  for 
example,  the  vibrations  of  the  corpuscles;  these  may  be 
divided  into  two  sets.  The  first  set  consists  of  those 
arising  from  the  rotation  of  the  corpuscles  around  their 
orbits.  If  all  the  corpuscles  in  an  atom  have  the  same 
angular  velocity,  the  frequency  of  the  vibrations  produced 


AERANGEMENT   OF   CORPUSCLES   IN   ATOM.     113 

by  the  rotation  of  the  ring  of  corpuscles  is  proportional  to 
the  number  of  corpuscles  in  the  ring;  and  thus  in  the 
spectrum  of  each  of  the  elements  corresponding  to  the 
arrangements  of  corpuscles  found  in  a  vertical  column  in 
the  Table,  there  would  be  a  series  of  lines  whose  frequencies 
would  be  in  a  constant  ratio  to  each  other,  this  ratio  being 
the  ratio  of  the  numbers  of  corpuscles  in  the  various 
rings. 

The  second  set  of  vibrations  are  those  corresponding  to 
the  displacement  of  a  ring  from  its  circular  shape.  If  the 
distance  of  a  corpuscle  from  the  nearest  member  in  its  own 
ring  is  small  compared  with  its  distance  from  its  nearest 
neighbour  on  another  ring,  the  effect  of  the  outer  ring  \vill 
only  "  disturb  "  the  vibrations  of  the  ring  without  altering 
their  fundamental  character.  Thus  we  should  expect  the 
various  elements  in  a  vertical  column  to  give  corresponding 
groups  of  associated  lines.  We  might,  in  short,  expect  the 
various  elements  corresponding  to  the  arrangements  of  the 
corpuscles  contained  in  the  same  vertical  column,  to  have 
many  properties,  chemical  as  well  as  physical,  in  common. 
If  we  suppose  that  the  atomic  weight  of  an  element  is 
proportional  to  the  number  of  corpuscles  contained  in  its 
atom, — and  we  shall  give  later  on  evidence  in  favour  of  this 
view, — we  may  regard  the  similarity  in  properties  of  these 
arrangements  of  corpuscles  in  the  same  vertical  column  as 
similar  to  a  very  striking  property  of  the  chemical  elements, 
i.e.,  the  property  expressed  by  the  periodic  law.  We 
know  that  if  we  arrange  the  elements  in  the  order  of 
their  atomic  weights,  then  as  we  proceed  to  consider  the 
elements  in  this  order,  we  come  across  an  element — 
say  lithium — with  a  certain  property  ;  we  go  on,  and  after 
passing  many  elements  which  do  not  resemble  lithium, 
we  come  to  another,  sodium,  having  many  properties  in 
common  with  lithium;  then,  as  we  go  on  we  lose  these 
properties  for  a  time,  coming  across  them  again  when  we 
arrive  at  potassium,  and  so  on.  We  find  here  just  the 
same  recurrence  of  properties  at  considerable  intervals 
that  we  should  get  if  the  atoms  contained  numbers  of 

T.M.  i 


114     THE    CORPUSCULAR   THEORY   OF   MATTER. 

corpuscles  proportional  to  their  atomic  weight.  Consider 
a  series  of  atoms,  such  that  the  atom  of  the  £>th  member 
is  formed  from  that  of  the  (p— l)th  by  the  addition  of  a 
single  ring,  i.e.,  is  a  compound,  so  to  speak,  of  the  (p— l)th 
atom  with  a  fresh  ring.  Such  a  series  would  belong  to 
elements  which  are  in  the  same  group  according  to  the 
periodic  law,  i.e.,  these  elements  form  a  series  which,  if 
arranged  according  to  Mendeleef's  table  would  all  be  in 
the  same  vertical  column. 

The  properties  of  these  configurations  of  corpuscles  have 
further  analogies  with  the  properties  of  real  atoms.  To 
illustrate  this  let  us  consider  the  properties  of  all  the 
configurations  of  corpuscles  which  have  20  corpuscles  in  the 
outside  ring.  The  smallest  number  of  corpuscles  which 
has  an  outer  ring  of  20  is  59 ;  in  this  case  the  number  of 
corpuscles  inside  the  ring  is  only  just  sufficient  to  make 
the  outer  ring  stable,  this  ring  will  therefore  be  on  the 
verge  of  instability,  and  when  the  corpuscles  in  the  ring 
are  displaced  the  forces  of  restitution  urging  them  back 
to  their  original  positions  will  be  small.  Thus,  when  this 
ring  is  subject  to  disturbances  from  an  external  source,  a 
corpuscle  will  easily  be  detached  from  it,  and  the  group 
will,  by  losing  a  negatively  electrified  corpuscle,  acquire  a 
charge  of  positive  electricity;  the  group  will  thus  resemble 
the  atom  of  a  strongly  electropositive  element.  When  we 
pass  from  59  to  60  corpuscles  the  outer  ring  is  more  stable 
because  there  are  more  corpuscles  inside  it ;  the  corre- 
sponding atom  will,  therefore,  not  be  so  strongly  electro- 
positive as  that  containing  only  59  corpuscles.  The 
addition  of  each  successive  corpuscle  will  make  it  more 
difficult  to  detach  corpuscles  from  the  outer  ring,  and  will, 
therefore,  make  the  corresponding  atom  less  electro-positive. 
The  increase  in  the  stability  of  the  ring,  and  consequently 
in  the  electro-negative  character  of  the  corresponding  atom, 
will  go  on  increasing  until  we  have  as  many  as  67  corpuscles 
in  the  group,  when  the  stability  of  the  outer  ring  will  be  a 
maximum.  A  great  change  in  the  properties  of  the  group 
will  occur  when  the  number  of  corpuscles  increases  from 


AEEANGEMENT   OF   COEPUSCLES   IN   ATOM.     115 

67  to  68,  for  with  68  corpuscles  the  number  in  the  outer 
ring  is  21 ;   these  21  corpuscles    are,  however,  only  just 
stable,  and,  like  the  outer  ring  of  20  in  the  arrangement  of 
59  corpuscles,  would  readily  lose  a  corpuscle.     The  atom 
corresponding   to  this    arrangement   would,   therefore,  be 
strongly  electro-positive. 

The  properties  of  the  groups  of  59  and  67  corpuscles, 
which  are  respectively  at  the  beginning  and  end  of  the 
series  which  has  20  corpuscles  in  the  outer  ring,  deserve 
especial  consideration.  The  arrangement  of  corpuscles  in 
the  group  of  59,  though  near  the  verge  of  instability  and 
therefore  very  liable  to  lose  a  negative  corpuscle  and  thus 
acquire  a  positive  charge,  would  not  be  able  to  retain  this 
charge.  For  when  it  had  lost  a  corpuscle  the  58  corpuscles 
left  would  arrange  themselves  in  the  grouping  corresponding 
to  58  corpuscles,  which  is  the  last  to  have  an  outer  ring  of 
19  corpuscles;  this  ring  is  therefore  exceedingly  stable,  so 
that  no  further  corpuscles  would  escape  from  it,  while  the 
positive  charge  on  the  system  due  to  the  escape  of  the 
59th  corpuscle  would  attract  the  surrounding  corpuscles. 
Thus  this  arrangement  could  not  remain  permanently 
charged  with  positive  electricity,  for  as  soon  as  one 
corpuscle  escaped  it  would  be  replaced  by  another.  If, 
however,  corpuscles  were  shot  into  the  arrangement  of  59 
from  outside,  each  additional  corpuscle  would  increase  the 
stability  of  the  system  until  the  number  reached  67 ;  the 
arrangement  corresponding  to  68  would  be  very  unstable, 
so  when  this  number  was  reached  the  system  would  lose 
corpuscles.  Thus  a  charge  of  8  units  of  negative  electricity 
could  be  forced  into  this  group,  which  would  correspond, 
therefore,  to  an  atom  with  a  valency  0  for  a  positive  charge, 
and  a  valency  8  for  a  negative  one. 

Let  us  now  consider  the  properties  of  the  group  of  67 
corpuscles.  The  outer  ring  of  this  would  be  very  stable, 
but  if  an  additional  corpuscle  were  added  to  the  group  the 

68  corpuscles  would  arrange  themselves  with  a  ring  of  21 
on  the  outside,  as  68  is  the  smallest  number  of  corpuscles 
with  an  outer  ring  of  21  ;  the  ring  is  very  unstable,  and 

i  2 


116     THE    COEPUSCULAE   THEOEY   OF   MATTER 

easily  loses  the  corpuscle  it  has  gained,  thus  the  arrange- 
ment could  not  permanently  be  negatively  charged — it  would 
act  like  the  atom  of  an  element  of  no  electro-negative 
valency.  On  the  other  hand,  the  arrangement  would  be 
stable  if  one,  two,  three  up  to  eight  corpuscles  were  abstracted 
from  it,  although  from  the  firmness  with  which  they  are 
held  this  detachment  of  corpuscles  would  be  difficult; 
as  each  corpuscle  abstracted  leaves  the  arrangement  with 
a  positive  charge,  the  work  required  to  remove  the  succes- 
sive corpuscles  would  tend  to  increase.  This  tendency 
would  be  to  some  extent  compensated  by  the  diminishing 
stability  of  the  arrangements  66,  65,  64,... 59;  but  when  once 
59  is  reached,  not  only  have  we  to  overcome  the  positive 
charge,  but  also  the  great  stability  of  the  arrangement  of 
58  corpuscles,  so  that  eight  would  be  the  greatest  number  of 
corpuscles  we  could  hope  to  remove  from  the  group;  thus 
the  atom  represented  by  this  group  would  have  an  electro- 
positive valency  represented  by  8,  while  its  electro-negative 
valency  is  zero. 

Let  us  now  consider  the  group  containing  60  corpuscles. 
This  will  be  the  most  electro-positive  of  the  series ;  it  can, 
however,  only  retain  permanently  a  positive  charge  of  one 
unit  of  electricity,  corresponding  to  the  removal  of  one 
corpuscle,  for  when  it  has  lost  two  corpuscles  we  should  have 
the  group  58  as  we  had  when  we  removed  one  corpuscle 
from  the  group  59  ;  and  in  the  present  case  the  group 
would  be  more  likely  to  attract  a  corpuscle  than  when 
we  started  from  59  instead  of  60,  for  it  would  have  a 
charge  of  two  positive  units  instead  of  one.  Thus  the 
atom  represented  by  the  group  of  60  would  have  an  electro- 
positive valency  of  one.  If  we  force  additional  corpuscles 
into  the  group  so  that  the  corpuscles  increase  to  61,  62,  63, 
67,  the  arrangements  become  more  and  more  stable  ;  when, 
however,  we  get  to  68  we  have  an  arrangement  which 
is  nearly  unstable  and  which  will  readily  give  off 
corpuscles.  Thus  seven  is  the  greatest  number  of  cor- 
puscles we  could  hope  to  force  into  this  group,  so  that  the 
atom  represented  by  it  would  have  an  electro-negative 


ARRANGEMENT   OF   CORPUSCLES   IN   ATOM.     117 

valency  of  seven.  We  have  seen  that  the  electro-positive 
valency  is  one. 

The  group  of  66  corpuscles  would  be  the  most  electro- 
negative of  the  series,  but  would  only  be  able  to  retain  a 
charge  of  one  unit,  for  if  it  acquired  two  units  the  group 
would  consist  of  68  corpuscles,  an  arrangement  which,  as  we 
have  seen,  rapidly  loses  its  corpuscles.  The  atom  correspond- 
ing to  the  group  66  will  thus  have  an  electro-negative  valency 
of  one.  We  see,  too,  that  seven  corpuscles  could  be  extracted 
from  the  group  without  destroying  its  stability  ;  thus  the 
atom  corresponding  to  this  group  would  have  an  electro- 
positive valency  seven. 

The  group  of  61  corpuscles  would  not  part  with  its 
corpuscles  so  readily  as  the  group  of  60,  but  on  the  other 
hand  it  could  afford  to  lose  two,  as  it  is  not  reduced  to  58 
corpuscles  until  it  has  lost  a  third  corpuscle,  and  58  is  the 
number  when  the  tendency  to  attract  and  retain  corpuscles 
would  suddenly  rise  ;  thus  the  atom  corresponding  to  the 
group  61  would  have  an  electro-positive  valency  of  2.  In 
the  same  way  as  before  we  see  that  it  could  find  room  for  6 
corpuscles,  so  that  the  corresponding  atom  might  have  an 
electro-negative  valency  of  6.  In  a  similar  way  we  see 
that  the  group  of  62  would  correspond  to  an  electro  -negative 
atom  with  an  electro-negative  valency  of  3  and  an  electro- 
positive valency  of  5.  The  group  63  is  an  atom  with  an 
electro-negative  valency  of  4  and  an  electro-positive  valency 
of  4.  Thus,  tabulating  our  results,  we  have  the  following 
properties  of  the  series  of  atoms  corresponding  to  the  groups 
containing  from  59  to  67  corpuscles  :  — 

No.  of  corpuscles     59     60     61     62     63     64     65     66     67 


Valency  {  +°  +1  +2  +3 

-8  -7  -6   -5   -4  +5  +6  +7  +8 

Electro-positive.         Electro-negative. 

This  sequence  of  properties  is  very  like  that  observed  in 
the  case  of  the  atoms  of  the  elements. 


118    THE   COEPUSCULAK   THEOEY  OF   MATTER 

Thus  we  have  the  series  of  elements — 

He.     Li.     Be.     B.      C.     N.     0.     F.     Ne. 
Ne.    Na.     Mg.    Al.     Si.    P.     S.     Cl.    Arc). 

The  first  and  last  element  in  each  of  these  series  has  no 
valency,  the  second  is  a  monovalent  electro-positive  element, 
the  last  but  one  a  monovalent  electro-negative  element, 
the  third  is  a  divalent  electro-positive  element,  the  last  hut 
two  a  divalent  electro-negative  element,  and  so  on. 

In  our  Table  we  have  assigned  two  valencies  to  the  element 
according  as  it  acts  as  an  electro-positive  or  an  electro- 
negative element,  and  we  notice  that  the  sum  of  these 
valencies  is  constant  and  equal  to  8.  It  is  interesting  to 
find  that  Abegg,1  from  purely  chemical  considerations,  shows 
that  the  valency  of  an  element  is  very  different  when  it  acts 
as  the  electro-positive  constituent  of  a  compound  from  its 
valency  when  it  is  the  electro-negative  constituent.  Thus 
chlorine  has  the  valency  1  in  a  compound  like  HCl,  in 
which  it  is  the  electro-negative  constituent,  but  has  much 
higher  valencies  when  combined  with  very  electro-negative 
elements  such  as  oxygen.  Iodine,  too,  is  another  striking 
instance;  it  is  monovalent  when  combined  with  electro- 
positive elements  like  the  metal,  but  has  a  much  higher 
valency  when  combined  with  more  electro-negative  elements 
as  in  the  compound  I  C15.  The  view  that  the  same  element 
is  sometimes  the  positive  constituent  and  in  other  combina- 
tions the  negative  constituent  of  a  compound  has  received 
further  confirmation  recently  by  some  remarkable 
experiments  made  by  Walden. 

The  sum  of  the  positive  and  negative  valencies  would 
;  depend  upon  the  number  of  corpuscles  assumed  to  be  in 
the  outer  ring.  If  we  take  the  number  in  the  outer  ring  to 
be  '20  the  sum  of  the  positive  and  negative  valencies  is  8 ; 
this  happens  to  agree  with  the  number  usually  assigned  to 
this  sum  by  chemists ;  this  agreement  with  the  results 
given  by  the  model  atom  is,  however,  quite  accidental. 

1  "  Zeitschrift  f iir  Anorganische  Chemie,"  39,  p.  330,  1904;  "Zeits- 
chrift  fiir  Physikalische  Chemie,"  43,  p.  385,  1903. 


ARRANGEMENT   OF   CORPUSCLES   IN   ATOM.     119 

It  may  not  be  out  of  place  here  to  again  emphasise 
the  statement  that  the  special  arrangement  of  corpuscles 
in  which  they  are  supposed  to  be  confined  to  one  plane, 
and  in  which  the  positive  electricity  attracts  them  with  a 
force  proportional  to  their  distance  from  a  fixed  point,  has 
been  chosen  because  it  is  the  one  most  amenable  to  mathe- 
matical treatment.  My  object  has  been  to  show  that  stable 
arrangements  of  corpuscles  would  have  many  properties  in 
common  with  real  atoms,  and  I  have  attempted  to  illustrate 
these  properties  by  considering  a  special  case  chosen  solely 
on  the  ground  of  simplicity.  The  number  of  corpuscles 
corresponding  to  any  particular  property  would  doubtless 
be  different  if  we  took  a  three-  instead  of  a  two-  dimensional 
distribution  of  corpuscles,  or  if  instead  of  supposing  the 
attractive  force  exerted  by  the  positive  electricity  to  vary 
directly  as  the  distance  from  a  fixed  point  we  assumed  that 
the  density  of  the  positive  electricity  inside  the  sphere  was 
not  uniform,  in  which  case  the  attraction  would  follow  a 
much  more  complicated  law. 

The  two-fold  valency  would  be  a  property  of  the  atom 
whatever  its  structure,  provided  that,  as  in  the  special  case 
of  corpuscles  confined  to  one  plane,  there  is  a  great  change 
of  stability  in  passing  through  certain  groups  of  corpuscles, 
the  number  of  corpuscles  in  these  critical  groups  being,  say, 
ATi,  Xz,  N3.  .  .  .  The  work  required  to  add  a  corpuscle  to,  or 
take  one  away  from,  a  group  of  corpuscles  would  be 
abnormally  great  when  the  change  in  the  number  of 
corpuscles  involved  the  passage  through  or  into  one  of  these 
critical  numbers ;  thus  these  critical  numbers  maybe  regarded 
as  barriers  which  cannot  easily  be  passed.  As  an  atom 
containing  7V2  +  n  corpuscles  could  lose  n  corpuscles  and 
gain  Ns  -  (A72  +  n)  without  crossing  one  of  these  barriers, 
such  an  atom  would  have  a  maximum  positive  valency  n 
and  a  maximum  negative  valency  N3  -  (N*  +  n). 

We  may  also  look  at  the  question  from  the  following  point 
of  view:  we  may  express  the  tendency  of  a  group  of  corpuscles 
to  shed  a  corpuscle  as  arising  from  the  equivalent  of  a  cor- 
puscular pressure  in  the  atom,  and  we  may  express  the 


120     THE    CORPUSCULAR   THEORY   OF   MATTER. 

preceding  result  by  saying  that  when  the  number  of  cor- 
puscles increases  through  one  of  the  values  N\,  N2,  N3  . . . , 
say  Ni,  the  corpuscular  pressure  abruptly  increases,  and 
then  falls  gradually  as  the  number  of  corpuscles  increases 
to  AT2,  when  again  the  pressure  abruptly  increases.  Thus 
for  a  group  of  corpuscles  intermediate  in  number  between 
NI  and  AT2  we  could  go  on  adding  corpuscles  without 
increasing  the  corpuscular  pressure  (though  of  course  we 
should  increase  the  repulsion  arising  from  the  negative 
charge  on  these  corpuscles)  until  we  reached  A72,  but  since 
at  NQ  the  corpuscular  pressure  rapidly  increases,  we  could 
not  without  great  difficulty  increase  the  number  of  cor- 
puscles to  A^  +  1.  Again,  we  could  take  away  corpuscles 
from  the  original  group  without  diminishing  the  corpus- 
cular pressure  until  the  number  of  corpuscles  is  reduced 
to  NI.  Since  the  corpuscular  pressure  abruptly  falls  at  this 
point  it  would  be  difficult  to  extract  another  corpuscle  from 
the  group.  Thus  if  N  the  number  of  corpuscles  in  this 
group  =  NI  +  n,  the  maximum  number  of  corpuscles  we 
could  extract  would  be  n,  i.e.,  the  maximum  positive  valency 
would  be  n,  while  the  greatest  number  we  could  add  would 
be  A"2  —  (Ari  +  n),  and  this  would  be  the  maximum  negative 
valency. 

FORCES    BETWEEN    THE    ATOMS.       CHEMICAL    COMBINATION. 

A  very  important  and  interesting  subject  of  investigation 
is  the  nature  of  the  forces  that  would  be  exerted  between 
groups  of  corpuscles  and  its  application  to  the  theory  of 
chemical  combination. 

We  shall  begin  by  considering  the  forces  between  two 
groups  in  some  simple  cases.  Let  us  begin  with  the 
simplest  of  all  when  we  have  a  single  corpuscle  at  the 
centre  of  a  sphere  of  positive  electrification.  Let  us  take 
two  such  systems  equal  in  all  respects,  then  as  long  as  one 
is  wholly  outside  the  other  there  will  be  neither  attraction 
nor  repulsion  between  the  systems ;  when,  however,  the 
spheres  cut,  as  in  Fig.  26,  the  systems  will  attract  each  other. 
To  see  this,  consider  the  action  of  the  system  A  on  B ;  there 


ARRANGEMENT   OF   CORPUSCLES   IN   ATOM.     121 

will  be  no  action  on  that  part  of  B  which  is  outside  A, 
while  the  action  on  the  part  of  the  positive  electricity 
of  B  which  is  inside  A  will  be  an  attraction  towards  the 
centre  of  A,  for  inside  a  sphere  the  force  due  to  the 
negative  corpuscle  at  the  centre  is  greater  than  that  due 
to  the  positive  electricity.  The  corpuscles  will  remain 
at  the  centres  of  their  respective  spheres  until  they 
come  so  close  together  that  the  centre  of  one  sphere 
lies  inside  the  other  sphere ;  when  this  stage  is  reached 
the  corpuscles  begin  to  be  displaced  and  are  pushed  apart 
so  as  to  be  outside  the  line  joining  the  two  centres.  In 
this  case  there  is  no  difference  in  the  electrification  of  the 
spheres  ;  we  cannot  say  that  one  is  positively  the  other 
negatively  electrified  ;  and  if  the  spheres  were  separated 


FIG.    26. 

after  having  been  together  they  would  each  be  neutral,  the 
positive  electricity  in  each  sphere  being  balanced  by  the 
negative  charge  at  the  centre.  We  thus  see  that  it  is 
possible  to  have  forces  electrical  in  their  origin  binding  the 
two  systems  together  without  a  resultant  charge  on  either 
system.  If,  however,  the  spheres  were  of  very  different 
size,  then  if  they  were  brought  close  enough  together  the 
two  corpuscles  would  go  inside  one  sphere  and  would 
remain  so  after  the  spheres  were  pulled  apart ;  thus  one 
sphere  would  be  positively,  the  other  negatively,  electrified. 
Lord  Kelvin  has  shown  that  it  is  the  smaller  sphere  that 
acquires  the  additional  corpuscle,  and  has  proved  that 
when  two  spheres  whose  radii  are  in  the  proportion  of 
3  to  1  are  gradually  brought  together,  the  corpuscle 
which  originally  was  at  the  centre  of  the  larger  sphere 


122    THE   COBPU8CULAR   THEORY   OF   MATTER. 

will  be  transferred  to  the  inside  of  the  smaller  when  the 
distance  between  the  centres  of  the  two  spheres  is  reduced 
to  between  2*6  and  2'7  times  the  radius  of  the  smaller 
sphere.  With  systems  containing  only  one  corpuscle  the 
only  way  in  which  one  system  can  differ  from  the  other  is  in 
the  size  of  the  sphere  of  positive  electrification.  The  pre- 
ceding result  is  a  special  case  of  the  general  principle  that  a 
transference  of  corpuscles  from  one  group  of  corpuscles  to 
another  different  group  may  occur  when  the  two  groups  are 
brought  close  together.  The  general  nature  of  this  effect 
may  be  understood  from  the  following  considerations.  If 
we  have  two  groups  of  corpuscles  A  and  B  such  that  the 
work  required  to  detach  a  corpuscle  from  A  is  less  than  that 
required  to  detach  one  from  B,  then  when  A  and  B  are 
brought  close  together  there  will  be  a  tendency  for  a 
corpuscle  to  go  from  A  into  B,  and  therefore  for  A  to  get 
positively,  B  negatively,  electrified.  The  system  A  corre- 
sponds— to  take  the  case  considered  on  page  117 — to  the 
groups  in  the  earlier  part  of  the  series  from  59  to  67,  the 
system  B  to  the  groups  in  the  later  part.  We  may  repre- 
sent this  effect  in  a  way  which  is  easily  handled,  by  saying 
that  inside  the  group  of  corpuscles,  or  atom,  there  is  a 
certain  corpuscular  pressure,  and  that  when  two  atoms  are 
brought  near  together  the  corpuscles  tend  to  pass  from  the 
atom  where  the  corpuscular  pressure  is  high  to  one  where 
it  is  low.  This  corpuscular  pressure,  by  which  we  represent 
the  electric  forces  inside  the  atom,  is  high  when  the  work 
required  to  detach  a  corpuscle  from  the  atom  is  small,  low 
when  this  work  is  large.  Thus  in  our  example  the  corpus- 
cular pressure  is  high  when  the  number  of  corpuscles  inside 
the  outer  ring  is  only  just  sufficient  to  make  that  ring 
stable,  while  it  is  low  when  the  number  of  corpuscles  inside 
is  considerably  greater  than  the  minimum  number  required 
for  equilibrium,  i.e.,  the  pressure  is  high  in  the  electro- 
positive elements,  low  in  the  electro-negative  ones.  We 
see,  too,  that  the  positive  valency  of  an  electro-positive 
element  is  the  greatest  number  of  corpuscles  it  can  lose 
before  the  corpuscular  pressure  suffers  a  great  diminution. 


ARRANGEMENT   OF  CORPUSCLES  IN  ATOM.     123 

To  take  an  illustration :  in  the  group  of  60  corpuscles  we  say 
that  the  corpuscular  pressure  is  high  since  there  is  only  one 
more  corpuscle  inside  the  outer  ring  than  the  minimum 
number  required  to  make  that  ring  stable ;  if,  however, 
two  corpuscles  were  to  leave  the  system,  the  number  would 
be  reduced  to  58,  and  the  group  58  has  an  outer  ring 
of  19  with  the  maximum  number  of  corpuscles  inside  it  ; 
the  system  has  thus  great  stability,  and  would  thus  be 
represented  by  one  with  a  low  corpuscular  pressure.  The 
negative  valency  of  an  electro-positive  element  is  the 
greatest  number  of  corpuscles  which  can  be  added  without 
producing  a  sudden  increase  in  the  corpuscular  pressure. 
Thus,  to  take  the  case  quoted  before,  if  eight  corpuscles  were 
added  to  the  group  of  60  corpuscles,  we  should  get  68 
corpuscles ;  now  68  is  the  smallest  number  of  corpuscles 
which  has  as  many  as  '21  corpuscles  in  the  outer  ring,  thus 
there  is  only  the  minimum  number  inside  required  for 
stability,  so  that  the  corresponding  corpuscular  pressure  is 
very  high,  while  if  we  added  seven  corpuscles  to  the  group 
of  60  we  should  have  67  corpuscles,  and  as  this  is  the  largest 
number  of  corpuscles  which  has  20  in  the  outside  ring,  there 
is  the  maximum  number  inside  the  ring ;  the  stability  is 
thus  very  great,  and  the  corresponding  corpuscular  pressure 
low.  We  thus  see  that  seven  is  the  greatest  electro-negative 
valency  for  the  group  60. 

The  negative  valency  of  the  electro-negative  elements, 
which  have  atoms  in  which  the  corpuscular  pressure  is  low, 
is  the  number  'of  corpuscles  which  can  be  added  without 
producing  a  sudden  increase  in  the  corpuscular  pressure. 
Thus,  to  take  an  example,  the  atom  corresponding  to  the 
group  of  66  corpuscles  has  an  electro-negative  valency  of  one, 
for  if  it  received  2  corpuscles  the  corpuscles  would  arrange 
themselves  like  the  group  68,  which,  as  we  have  seen,  has  a 
very  high  corpuscular  pressure. 

The  electro-positive  valency  of .  these  elements  is  the 
greatest  possible  number  of  corpuscles  which  can  be  taken 
from  them  without  producing  an  abrupt  diminution  in  the 
corpuscular  pressure.  Thus,  to  take  the  group  of  66,  if  we 


124     THE    CORPUSCULAR   THEORY   OF   MATTER. 

take  away  7  corpuscles  we  get  the  arrangement  correspond- 
ing to  59,  which  is  nearly  unstable,  and  in  which,  therefore, 
the  corpuscular  pressure  is  very  high.  If,  however,  we  take 
away  8  corpuscles,  we  have  only  58  left,  and  this  arrange- 
ment is  very  stable,  as  it  is  the  largest  number  of  corpuscles 
which  has  as  few  as  19  in  the  outer  ring,  so  that  the 
corpuscular  pressure  is  very  low ;  thus  the  corpuscular 
pressure  is  diminished  abruptly  when,  having  already 
detached  7,  we  detach  an  additional  corpuscle ;  hence  we  see 
that  the  electro-positive  valency  of  the  group  60  is  7. 

To  sum  up,  if  the  electro-positive  valency  of  an  atom  is 
n,  then  we  can  extract  n  corpuscles  without  diminishing 
the  corpuscular  pressure,  but  if  we  detach  an  additional 
corpuscle  the  corpuscular  pressure  will  suddenly  fall ;  if  the 
electro -negative  valency  of  an  atom  is  m,  we  can  add  m 
corpuscles  without  increasing  the  corpuscular  pressure,  but 
the  addition  of  the  (m  -f-  l)th  will  cause  a  large  increase  in 
the  pressure. 

Let  us  see  now  how  these  considerations  apply  to  the 
chemical  combinations  of  the  different  elements.  Let  us 
suppose  that  we  have  two  different  atoms  A  and  B  close 
together,  and  that  the  element  of  which  A  is  an  atom  is 
more  electro-positive  than  the  one  of  which  B  is  an  atom ; 
this  on  our  view  means  that  the  corpuscular  pressure  in  the 
atom  A  is  greater  than  that  in  B,  so  when  A  and  B  are  put 
close  together  a  corpuscle  will  tend  to  go  from  A  to  B,  and 
thus  A  would  get  positively,  B  negatively  electrified.  The 
loss  of  the  corpuscle  by  the  electro-positive  atom  would, 
if  its  positive  valency  were  greater  than  unity,  tend  to 
increase  the  corpuscular  pressure  in  A,  while  the  gain  of 
a  corpuscle  by  B  would,  unless  it  were  negatively  univalent, 
lower  its  corpuscular  pressure;  this  effect  would  tend  to 
make  the  flow  of  corpuscles  from  A  to  B  continue ;  on  the 
other  hand,  the  positive  electrification  on  A  and  the  negative 
on  B  would  tend  to  stop  the  flow.  Let  us  suppose  that  the 
electro-positive  valency  of  A  is  unity,  then  if  a  second  cor- 
puscle were  to  escape  from  A  the  corpuscular  pressure,  as  we 
have  seen  above,  would  fall  abruptly,  so  that  instead  of  the 


ARRANGEMENT   OF    CORPUSCLES    IN   ATOM.     125 

pressure  gradient  being  down  from  A  to  B  it  would  be  in  the 
opposite  direction,  and  the  corpuscle  would  come  back  ;  thus 
A  would  not  lose  more  than  one  corpuscle.  If  the  negative 
valency  of  B  were  unity  then  B  would  not  be  in  a  condition 
to  receive  more  than  one  corpuscle,  for  if  it  received  two 
the  corpuscular  pressure  would  suddenly  increase,  and  cor- 
puscles would  tend  to  leave  B  instead  of  coming  into  it ; 
if,  however,  B  had  an  electro-negative  valency  of  2  it 
could  receive  another  corpuscle  without  increase  in  pres- 
sure, and  though  it  could  not  receive  this  from  A,  if 
another  atom  A'  similar  to  A  were  brought  to  it,  a  cor- 
puscle might  flow  from  A'  into  B,  and  thus  B  would  get 
charged  with  two  units  of  negative  electricity,  A  and  A' 
each  having  a  positive  charge  of  one  unit ;  thus  B  might 
hold  by  the  electrostatic  attraction  two  atoms  A  and  A'  in 
combination.  It  could  not,  however,  hold  a  third  atom, 
because  if  another  atom  A",  similar  to  A  and  A',  were 
brought  up  to  it,  and  if  another  corpuscle  were  to  flow 
into  B,  the  corpuscular  pressure  in  B  would  experience  a 
large  increase,  since,  as  its  valency  is  only  two,  it  cannot 
receive  more  than  two  corpuscles  without  having  its  cor- 
puscular pressure  largely  increased.  Thus  B  can  hold  two, 
but  not  more  than  two,  univalent  atoms  in  combination  ; 
if,  however,  B  had  been  trivalent  instead  of  divalent,  it 
could  receive  3  corpuscles  without  increasing  the  corpuscular 
pressure,  so  that  a  corpuscle  might  flow  from  a  third  atom 
A"  into  B,  and  B  be  able  to  keep  3  atoms  A,  Ar,  A",  in 
combination.  It  must  be  noticed,  however,  that  the  trans- 
ference of  the  corpuscles  from  the  atoms  Ar,  A",  which  are 
supposed  to  come  into  the  neighbourhood  of  B  after  A  has 
transferred  its  corpuscles,  will  take  place  under  less  favour- 
able conditions  than  the  transference  of  the  corpuscle  from 
A,  the  atom  first  brought  into  its  neighbourhood.  For 
when  A  approached  B  both  were  supposed  uncharged,  but 
after  the  corpuscle  from  A  has  gone  into  JB,  B  has  a  nega- 
tive charge,  and  the  corpuscle  going  from  A'  will  have  to 
surmount  the  electrostatic  repulsion  due  to  the  charge. 
Again,  after  A'  has  discharged  its  corpuscle,  B  will  be 


126     THE   COKPUSCULAR   THEOEY  OF   MATTER, 

charged  with  two  units  of  negative  electricity,  and  the  cor- 
puscle going  from  A"  will  have  to  overcome  a  greater 
repulsion  than  that  experienced  by  the  corpuscle  from  A'. 
Thus  we  see  that  in  the  case  of  a  multivalent  atom  it  may 
be  more  difficult  to  fill  up  the  later  valencies  than  the  earlier 
ones.  The  existence  of  "  unsaturated  "  compounds,  such  as 
PC/3,  MnCl%,  may  be  taken  as  an  illustration  of  this 
point. 

Again,  this  difficulty  will  produce  the  most  marked 
effects  when  the  difference  of  corpuscular  pressure  tending 
to  drive  the  corpuscles  from  one  atom  to  the  other  is  small, 
i.e.,  when  the  elements  resemble  each  other  in  properties. 
We  should  thus  expect  that  the  valency  of  one  ele- 
ment towards  an  element  of  somewhat  similar  properties 
would  be  less  than  its  valency  towards  a  widely  dissimilar 
element. 

The  terms  electro-negative  and  electro-positive  are  only 
relative,  and  an  element  may  be  electro-positive  to  one 
substance  and  electro-negative  to  another.  It  would  appear 
from  the  preceding  considerations  that  the  valency  of  an 
element  where  it  is  acting  as  the  electro-negative  consti- 
tuent of  a  compound  may  be  very  different  from  the  valency 
when  it  is  the  electro-positive  constituent.  Thus,  to  take 
the  group  of  60  corpuscles  as  an  example,  when  it  is  in  com- 
bination with  a  more  electro-negative  element,  i.e.,  one 
where  the  corpuscular  pressure  is  lower,  it  can,  as  we  have 
seen,  only  lose  one  corpuscle,  i.e.,  its  electro-positive  valency 
is  one.  But  if  the  group  60  were  placed  near  a  group  G 
with  a  still  higher  corpuscular  pressure,  so  that  corpuscles 
flow  into  the  group  60  instead  of  flowing  out  of  it,  then, 
since  we  have  seen  that  the  corpuscular  pressure  of  the 
group  60  will  not  be  suddenly  increased  by  the  addition  of 
corpuscles  until  the  number  of  corpuscles  added  exceeds  7, 
we  see  that  the  group  of  60  might  receive  as  many  as  7 
corpuscles  from  such  groups  as  G,  and  would  therefore  have 
a  valency  7.  There  are  many  compounds  which  suggest  a 
difference  of  this  kind.  Thus  iodine  appears  monovalent 
in  the  compound  H  I,  in  which  it  is  the  electro-negative 


AEKANGEMENT   OF   COEPUSCLES   IN   ATOM.     127 

element,  while  it  is  sexavalent  in  the  compound  I  F6,  in 
which  it  is  probably  the  positive  element. 

We  see  that  on  these  views  the  valency  of  an  element  is 
not  a  constant  quantity ;  it  depends  on  whether  the  element 
is  the  electro-positive  or  electro-negative  constituent  of  the 
compound,  and  even  when  the  sign  of  its  charge  is  the 
same,  on  the  nature  of  the  element  with  which  it  is  in 
combination,  an  element  having  a  smaller  valency  when 
combined  with  one  of  similar  properties  than  when  in  com- 
bination with  one  from  which  it  differs  more  widely. 

In  the  cases  of  chemical  combination  we  have  considered, 
we  have  supposed  that  there  is  a  transference  of  corpuscles 
from  one  atom  to  the  other,  and  that  the  attraction  between 
the  positive  and  negative  electrification  resulting  from  this 
transference  helps  to  bind  together  the  elements  in  the 
compound.  The  case,  however,  of  two  equal  spheres,  each 
with  a  single  corpuscle  at  its  centre,  considered  on  p.  121, 
shows  that  there  may  be  attractions  between  atoms  con- 
sisting of  groups  of  corpuscles  without  any  transference  of 
corpuscles,  i.e.,  when  neither  atom  gets  charged  with 
electricity.  A  very  important  question  arises  when  we  con- 
sider the  combination  of  two  similar  atoms  in  the  molecule 
of  an  elementary  gas  :  is  there  or  is  there  not  a  transference 
of  electricity  in  this  case — i.e.,  does  one  atom  acquire  a  charge 
of  positive,  the  other  of  negative,  electricity  ?  If  two  similar 
atoms  or  groups  of  corpuscles  are  brought  together,  a 
symmetrical  distribution  of  corpuscles,  i.e.,  one  in  which 
there  is  no  transference  of  corpuscles,  will  certainly  be  one  of 
equilibrium.  The  question,  however,  is,  is  the  equilibrium 
stable?  We  can  easily  give  examples  in  which  the  equili- 
brium of  symmetrical  arrangements  is  unstable.  Take  for 
example  the  case  of  two  electrified  drops  of  water  placed 
in  a  vessel  which  they  very  nearly  fill,  let  condensation 
on  the  sides  of  the  vessel  be  prevented,  so  that  the  vapour 
from  one  drop  condenses  on  the  other.  There  will  be 
equilibrium  if  the  drops  are  equal,  but  this  equilibrium 
will  be  unstable,  for  if  one  drop  were  to  differ  ever  so 
little  in  size  from  the  other,  the  smaller  drop  would  evaporate 


128     THE    COKPUSCULAE   THEOKY  OF   MATTER 

more  rapidly  than  the  larger ;  thus  the  big  drop  would  get 
bigger  by  condensation,  and  the  little  drop  smaller.  When 
the  little  drop  got  below  a  certain  size  the  electrical  charge 
would  so  lower  its  vapour  pressure  that  it  would  sink  to 
that  of  the  big  drop,  and  there  would  be  equilibrium,  and  in 
this  case  the  equilibrum  would  be  stable,  for  if  the  little 
drop  were  to  get  smaller  its  vapour  pressure  would  diminish 
so  rapidly  that  water  would  condense  on  it  and  it  would 
grow  bigger;  while  if  it  got  bigger  the  vapour  pressure 
would  increase  and  the  drop  would  become  smaller.  Thus 


FIG.  27. 

two  charged  drops  of  water,  equal  in  all  respects  to  begin 
with,  will  not  remain  equal,  and  the  stable  configuration  will 
not  be  two  equal  drops,  but  one  big  and  one  little  drop. 

Another  example  in  which  the  forces  concerned  bear  a 
somewhat  close  analogy  to  those  at  work  in  the  atom  is  the 
following : — 

Let  us  represent  an  atom  in  the  normal  state  by  a  closed 
glass  vessel  partly  filled  with  water  and  suspended  from  a 
spring  balance.  To  represent  the  effect  of  the  influence  of  an 
atom  on  an  equal  atom  near  to  it,  let  us  suppose  that  the 
water  in  two  similar  vessels  is  connected  by  a  syphon,  as  in 


ARRANGEMENT  OF   COEPUSCLES  IN  ATOM.     129 

Fig.  27,  then  though  there  could  be  equilibrium  without  any 
transference  of  water  from  A  to  B,  it  is  easy  to  see  that  the 
equilibrium  would  be  unstable.  For  suppose  a  little  water 
were  to  flow  from  A  to  B,  this  would  make  B  heavier  and  it 
would  descend ;  the  water  in  B  would  now  be  at  a  lower  level 
than  that  in  A,  so  that  the  water  instead  of  flowing  back  as 
it  would  if  the  equilibrium  were  stable  would  continue  to 
flow  into  B,  and  the  flow  would  go  on  until  the  pressure 
due  to  the  compression  of  the  air  confined  above  B  was 
sufficient  to  balance  the  pressure  difference  arising  from 
the  difference  of  level.  Thus  the  coupling  up  of  the  two 
would  produce  a  transference  of  water  from  the  one  to  the 
other,  or,  if  we  suppose  that  the  water  represents  an  electric 
charge,  the  one  would  be  positively,  the  other  negatively, 
electrified. 

In  the  case  of  groups  of  corpuscles  we  should  have  forces 
between  the  groups  with  somewhat  the  same  properties  as 
those  discussed  in  the  last  example.  Thus,  take  one  of 
the  arrangements  discussed  on  page  117,  say  the  group  of 
62;  this  is  more  stable  than  the  group  of  61  and  less  stable 
than  that  of  63,  or,  as  we  have  expressed  it,  the  corpuscular 
pressure  in  the  group  62  is  less  than  that  in  61  and  greater 
than  that  in  63.  Now  suppose  two  groups  each  containing 
62  were  brought  near  together,  and  suppose  a  corpuscle 
were  transferred  from  one  group  to  the  other,  so  that  one 
group  contained  61  and  the  other  63,  as  the  pressure  in  the 
group  61  is  greater  than  that  in  the  group  containing  63, 
the  corpuscles  would  tend  to  go  on  flowing  from  61  to  63 
instead  of  coming  back,  that  is,  if  one  got  by  chance  a  nega- 
tive charge,  that  charge  would  tend  to  increase  until  the 
electrostatic  repulsion  due  to  the  negative  charge  was 
sufficient  to  counterbalance  the  effect  of  corpuscular  pres- 
sure. Thus  we  see  in  this  case  that  the  stable  configuration 
for  two  groups  placed  within  range  of  each  other's  action  is 
one  in  which  there  is  a  positive  charge  on  one  group  and  a 
negative  charge  on  the  other.  If  we  apply  these  considera- 
tions to  the  case  of  atoms,  we  arrive  at  the  conclusion 
that  when  two  atoms  of  the  same  kind  come  so  near 

T.M.  K 


130  THE  CORPUSCULAR  THEORY  OE  MATTER. 

together  as  to  exert  appreciable  forces  on  each  other  one  of 
them  may  become  positively,  the  other  negatively,  electrified. 
Thus  the  two  atoms  in  a  diatomic  molecule  of  an  elemen- 
tary gas  may  be  oppositely  electrified,  and  the  forces 
which  hold  two  similar  atoms  together  in  the  molecule  of 
an  elementary  substance  may  be  quite  similar  to  those 
which  hold  together  two  dissimilar  atoms  in  the  molecule 
of  a  compound.  The  maximum  charge  which  an  atom 
could  receive  when  in  combination  with  an  atom  of  the 
same  kind  would  be  the  same  as  the  maximum  charge  when 
combined  with  an  atom  of  a  different  kind,  and  would  be 
determined  by  its  valency.  We  can,  as  the  example  on 
page  121  shows,  conceive  of  attractions  between  atoms  of 
the  same  kind  even  when  the  atoms  do  not  get  oppositely 
electrified ;  but  the  properties  of  molecules  of  simple  and 
compound  gases  seem  to  testify  in  favour  of  the  view  that 
the  forces  which  hold  the  similar  atoms  together  in  the 
molecule  of  an  elementary  gas  are  of  the  same  character  as 
those  at  work  binding  together  dissimilar  atoms  in  the 
molecule  of  a  compound.  Thus,  for  example,  gases  such  as 
helium  or  argon,  whose  atoms  do  not  combine  with  the 
atoms  of  other  gases  to  form  compounds,  do  not  combine 
with  each  other  to  form  diatomic  molecules.  Again,  when, 
as  in  carbon  compounds,  we  have  atoms  of  the  same  kind  in 
combination  with  each  other,  the  bonds  uniting  a  carbon 
atom  to  another  carbon  atom  are  treated  as  following  the 
same  laws  as  to  valency  as  those  which  bind  the  carbon 
atoms  to  atoms  of  a  different  kind. 

The  view  that  the  atoms  in  a  molecule  are  oppositely 
charged  receives  support  from  some  experiments  made  by 
Walden,  in  which  it  was  found  that  electrolytic  conduction 
took  place  when  bromine  and  iodine  were  dissolved  in 
certain  solvents,  the  bromine  or  iodine  appearing  at  both 
electrodes,  the  results  being  consistent  with  the  view  that 
the  bromine  or  iodine  molecules  are  dissociated  into  the 
ions  Br+,  Br_  or  I+,  I_.  The  view  is  also  supported 
by  the  fact  that  when  the  molecules  of  an  elementary  gas 
are  dissociated  by  heat,  as  in  the  case  of  iodine  vapour,  the 


AEEANGEMENT   OF   COEPUSCLES   IN   ATOM.     131 

electric  conductivity  of  the  dissociated  gas  is  very  high, 
showing  that  there  are  large  quantities  of  both  positive 
and  negative  ions  present  in  the  dissociated  gas. 

The  optical  properties  of  gases,  especially  the  refractive 
index  and  the  dispersion,  would,  as  we  shall  see,  be  largely 
influenced  by  opposite  charges  existing  on  the  atoms  in 
the  molecule — in  fact,  we  should  expect  the  dispersion  in  a 
gas  in  which  the  two  atoms  in  the  molecule  carry  opposite 
charges  would  be  of  quite  a  different  order  from  the  dis- 
persion of  a  gas  whose  molecules  consist  of  uncharged 
atoms.  The  numerous  experiments  which  have  been  made 
on  the  dispersion  of  gases  do  not  afford  any  evidence  of  the 
existence  of  any  wide  divergence  between  the  dispersion  of 
compound  and  of  elementary  gases;  hence  we  may  conclude 
that  if  the  atoms  in  the  molecules  of  the  compound  gas 
are  charged  with  electricity,  the  atoms  of  the  molecules  of 
elementary  gases  are  also  charged. 

The  positive  charge  on  one  atom  and  the  negative  charge 
on  the  other  produces  a  difference  between  the  atoms  which 
might  lead  to  a  want  of  symmetry  in  compounds  which 
from  their  formulae  appear  perfectly  symmetrical.  Thus, 
to  take  an  example,  ethane  is  represented  by  the  formula — 

H  H 

IL—C C~-H 

H  H 

but  if  we  regard  the  coupling  up  of  one  carbon  atom  with 
another  as  accompanied  by  a  transference  of  a  corpuscle 
from  the  one  atom  to  another,  the  two  carbon  atoms  will 
not  carry  equal  charges.  If  all  the  hydrogen  atoms  are 
charged  with  one  unit  of  positive  electricity  one  of  the 
carbons  will  have  a  charge  of  four  units  of  negative 
electricity  while  the  other  will  only  have  two  units ;  thus  of 
the  two  systems  C  H3,  one  will  carry  a  positive  charge, 
the  other  a  negative  one. 

This  would  involve  the  possibility  of  two  isomeric  com- 
pounds of  the  composition  C%  H5  Cl,  one  when  the  chlorine 

K  2 


132     THE    COKPUSCULAK  THEOKY  OF   MATTER, 

is  attached  to  the  carbon  atom  with  the  charge  4,  the 
other  when  it  is  attached  to  the  carbon  atom  with  the 
charge  2.  I  am  not  aware  that  there  is  any  evidence 
of  the  existence  of  isomeric  forms  of  C%  H5  Cl ;  it 
might  be  expected  that  even  if  both  were  stable  they 
would  have  very  different  degrees  of  stability.  It  must 
be  remembered  that  in  considering  the  possibility  of 
the  existence  of  isomers  from  purely  geometrical  con- 
siderations all  questions  as  to  stability  are  ignored,  so 
that  isomers  which  are  indicated  by  geometry  as  possible 
may  be  dynamically  unstable  and  thus  incapable  of 
preparation. 

If  we  consider  compounds  in  which  the  carbon  atoms  are 
linked  by  more  bonds  than  one  we  see  the  possibility  from 
geometrical  considerations  of  isomers  among  the  hydro- 
carbons themselves.  Thus  consider  ethylene — 


in  which  the  carbon  atoms  are  united  by  double  bonds.  If  we 
regard  each  bond  as  involving  the  transference  of  a  corpuscle 
from  one  carbon  atom  to  the  other,  we  might  have  two 
isomers ;  in  one  the  transference  of  the  corpuscle  having 
been  in  the  same  direction  along  each  bond,  one 
carbon  atom  has  lost  and  the  other  gained  two  units  of 
negative  electricity;  in  the  other  modification  the  transfer- 
ence of  corpuscles  has  been  in  one  direction  along  one 
bond  and  in  the  opposite  direction  along  the  other,  so 
that  on  the  whole  the  charge  on  the  carbon  atom  has 
not  been  affected  by  the  linkage.  This  form  of  com- 
pound is  much  more  symmetrical  than  the  preceding 
and  will  not  give  rise  to  so  many  isomers  when  chlorine 
is  substituted  for  hydrogen.  Again,  even  with  single 
linkage  between  the  carbon  atoms  we  might  have  isomers 
among  the  hydro-carbons  when  the  number  of  carbon 


AEEANGEMENT   OF   COEPUSCLES   IN   ATOM.     183 


atoms  is  greater  than  two.    Thus  consider  the  hydrocarbon 
represented  by  the  formula — 


H 


II- 


H 


-C\ 


H 


•H 


H 


H        H 


We  might  have  one  compound  in  which  the  linkage  between 
Ci  €2  caused  a  corpuscle  to  go  from  C\  to  <72,  and  that 
between  C2  C3  sent  a  corpuscle  from  (72  to  Ca;  the  result 
would  be  that  €3  is  negatively  and  Cl  positively  charged 
relatively  to  C2.  Or  again,  if  a  corpuscle  went  as  before 
from  Ci  to  C^,  but  the  linkage  between  C2  and  €3  caused  a 
corpuscle  to  go  from  C3  to  C2,  instead  of  from  <72  to  <73, 
Ci  and  C3  would  be  both  charged  positively  relatively  to  <72, 
and  this  would  differ  from  the  preceding  arrangement.  We 
should  get  a  third  case  if  the  linkage  between  the  carbon 
atoms  caused  one  corpuscle  to  go  from  (72  to  Cl  and  another 
from  C2  to  (73;  in  this  case  both  Ci  and  <73  would  be  charged 
negatively  relative  to  <72.  We  should  of  course  get  a  larger 
number  of  isomers  if  we  had  a  large  number  of  carbon 
atoms. 

We  thus  see  that  in  the  carbon  compounds  the  charge 
carried  by  the  carbon  atom  will  depend  upon  whether  the 
elements  combined  with  the  carbon  are  electro-positive  or 
electro-negative  with  respect  to  that  element.  Thus 
in  the  compound — 

E 


H- 


-C- 


G 

where   C  is  the  carbon  atom    and  E  F  G  -H"  are  mono- 
valent  atoms  of  other  elements,  if  these  elements  are  all 


134  THE  CORPUSCULAR  THEORY  OF  MATTER. 

electro-positive  with  regard  to  carbon,  the  carbon  atom 
will  carry  a  charge  of  4  units  of  negative  electricity,  while 
if  they  are  all  electro-negative  it  will  carry  a  charge  of 
4  units  of  positive  electricity ;  if  one  is  electro-positive  the 
others  electro-negative  the  charge  on  C  will  be  2  units  of 
positive,  and  so  on.  Thus  the  properties  of  the  carbon  atom 
will  depend  upon  the  elements  with  which  it  is  in  combina- 
tion. This  variation  in  the  properties  might  be  difficult  to 
detect  in  the  saturated  compound,  but  might  be  expected  to 
exert  more  influence  in  organic  radicles  such  as — 


which  enter  into  compounds  by  the  linkage  of  their  carbon 
atoms  with  other  atoms;  the  facility  with  which  this  linkage 
takes  place  might  be  gravely  affected  by  the  sign  and  magni- 
tude of  the  electric  charge  carried  by  the  carbon  atom,  and 
this  seems  to  be  in  accordance  with  the  results  of  observa- 
tions, as  Van  t  'Hoff  in  his  "  Ansichten  iiber  Organischen 
Chemie  "  gives  several  instances  of  changes  produced  in  the 
carbon  atom  in  organic  radicles  by  changes  in  the  elements 
with  which  it  is  in  combination. 

A  system  of  four  atoms,  each  possessing  unit  positive  and 
unit  negative  valency  rigidly  attached  to  each  other  and 
forming  the  four  corners  of  a  regular  tetrahedron,  would 
possess  the  same  chemical  properties  as  the  carbon  atom ; 
two  such  atoms  could  be  united  by  one,  two,  or  three  bonds, 
while  the  free  valencies  not  satisfied  by  the  connection 
between  the  atoms  would  be  satisfied  by  any  univalent 
atoms  whether  electro-positive  or  electro-negative. 

We  might  also  expect  to  see  traces  of  the  influence  of  the 
properties  of  the  atom  we  have  been  considering  on  the 
boiling  points  of  liquids  or  on  the  temperature  at  which 
gases  are  liquefied,  as  these  depend  on  the  forces  exerted 
between  different  molecules  of  the  substance,  an  increase 


ARKANGEMENT   OF   COEPUSCLES   IN   ATOM.     135 

in  these  forces  tending  to  raise  the  boiling  point  of  a  liquid 
and  increase  the  ease  with  which  a  gas  is  liquefied.  These 
forces  also  influence  the  connection  between  the  pressure  and 
volume  of  a  gas ;  they  are,  for  example,  responsible  for  the 
term  a/r*  in  Van  der  Waals  equation — 


and  from  the  values  of  a  we  can  deduce  a  measure  of  the 
intensity  of  these  forces.  It  is  more  satisfactory  to  take  a 
as  the  index  of  these  forces  than  to  use  the  boiling  point  or 
even  the  critical  temperature  for  this  purpose,  as  the 
latter  depend  upon  b  the  size  of  the  molecule  as  well  as 
upon  the  inter-molecular  forces.  Another  useful  measure 
of  the  strength  of  their  forces  is  the  amount  of  heat  required 
to  turn  one  gramme  molecule  of  the  substance  from  the 
liquid  into  the  gaseous  state,  as  this  quantity  is  directly 
proportional  to  the  work  required  to  drag  away  a  molecule 
of  compound  against  the  attraction  exerted  upon  it  by  a 
slab  of  the  substance  in  the  liquid  state. 

Let  us  now  endeavour  to  picture  to  ourselves  how  these 
forces  may  arise.  When  an  atom  in  a  compound  is  "  un- 
saturated  "  we  should  expect  it  to  exert  considerable  attrac- 
tion on  other  atoms,  because  we  know  that  under  suitable 
conditions  it  is  able  to  attract  some  other  atoms  so  firmly 
that  they  become  permanently  attached  to  it.  But  even 
when  an  atom  in  a  molecule  is  "  saturated,"  i.e.,  when  no 
transference  of  corpuscles  to  or  from  it  is  possible,  forces 
between  two  neighbouring  atoms  may  exist  although  they 
are  not  able  to  drag  the  corpuscles  from  one  atom  to  another 
and  thus  establish  a  "chemical  bond"  between  the  atoms. 
The  forcebetween  two  atoms  will,  among  other  things,  depend 
upon  the  ease  with  which  the  corpuscles  can  move  about 
in  the  atoms,  for  just  the  same  reason  that  the  force  between 
two  oppositely  electrified  bodies  is  greater  when  these  bodies 
are  conductors  of  electricity  in  which  the  electricity  can 
move  about  and  electrostatic  induction  come  into  play, 


186  THE  COEPUSCULAE  THEOEY  OF  MATTEE. 

than  when  they  are  insulators  in  which  the  electricity  is 
fixed. 

If  an  atom  is  unsaturated,  it  means  that  there  are  still 
some  corpuscles  which  have  comparative  freedom  of  motion, 
for  under  suitable  conditions  these  can  be  moved  into  or  out 
of  the  atom  when  it  acquires  its  maximum  valency ;  thus 
we  should  expect  that  a  molecule  containing  an  unsafcurated 
atom  would  exert  considerable  forces  upon  other  molecules, 
and  thus  would  tend  to  make  the  gas  depart  from  Boyle's 
law  and  to  be  easily  liquefiable.  But  even  when  all  the 
atoms  in  the  molecule  are  saturated  and  the  valency  cor- 
puscles transferred  there  may  still  remain  some  mobility  of 
the  corpuscles,  although  not  sufficient  to  enable  them  to  get 
clear  of  the  atom ;  this  mobility  may  not  be  the  same  for 
the  atoms  of  the  different  elements,  and  may  be  different 
for  the  same  atom  according  as  it  is  exerting  positive  or 
negative  valency ;  in  other  words,  the  attraction  of  an  atom 
may  not  be  wholly  exhausted  when  its  valency  is  satisfied, 
and  the  residual  attraction  may  depend  not  only  upon  the 
nature  of  the  atom  but  also  upon  whether  it  is  exerting  its 
positive  or  negative  valencies. 

Let  us  take  some  examples.  Marsh  gas  C  Hi  is  a  gas 
which  is  not  easily  liquefied  and  in  which  the  attraction 
between  the  molecules  is  small ;  when,  however,  one  of  the 
hydrogen  atoms  is  replaced  by  0  H  we  get  methyl  alcohol, 
which  is  a  liquid  at  ordinary  temperatures  and  whose 
molecules  exert  considerable  attractions  on  each  other.  If, 
as  many  chemists  maintain,  oxygen  may  be  tetravalent,  then 
the  oxygen  in  C  H3  0  H  is  unsaturated,  and  can  exert  con- 
siderable attractions  on  other  atoms ;  the  hydrogen  which  it 
replaced  was  saturated,  and  could  not  therefore  exert  nearly 
such  large  attractions.  Again,  chlorine  is  very  far  from 
being  a  perfect  gas,  and  the  wide  deviations  it  shows  from 
Boyle's  law  indicates  that  the  residual  attractions  between 
the  molecules  is  very  considerable.  Chlorine  seems  to  retain 
this  residual  attraction  when  in  combination  with  other 
elements,  for  the  result  of  replacing  the  hydrogen  atoms  in 
C  Hi  by  chlorine  atoms  as  in  the  compounds  C  H3  Cl, 


ARRANGEMENT   OF   COKPUSCLES  IN  ATOM.     137 

C  H%  Clz,  C  H  C13,  C  C/4,  is  to  produce  substances  which 
depart  more  and  more  from  being  perfect  gases  as  their 
chlorine  content  is  increased  ;  indeed,  the  later  ones  are 
fluid  at  ordinary  temperatures.  Assuming  that  the 
hydrogen  atom  is  positively,  and  the  chlorine  atom  nega- 
tively, charged,  the  charge  carried  by  the  carbon  atom  varies 
from  —  4  in  C  Hi  to  +  4  in  C  Cl±,  and  it  is  an  interesting 
subject  of  inquiry  whether  the  residual  attraction  of  the 
carbon  atom  is  affected  by  the  charge  ;  the  residual  attraction 
of  chlorine,  however,  is  so  great  that  it  would  probably  swamp 
the  effect  of  the  carbon.  Since  the  residual  attraction  of 
hydrogen  is  very  small  we  should  have  a  better  chance 
of  detecting  changes  in  the  residual  attraction  of  carbon  if 
we  worked  with  compounds  containing  nothing  but  hydrogen 
in  addition  to  the  carbon.  A  study  of  the  values  of  a  in  Van 
der  Waals'  equation  for  such  compounds  as  C%  H6,  C%  H±, 
€2  H2,  in  which  the  carbon  atoms  carry  charges  which  vary 
from  one  compound  to  another,  might  throw  some  light  on  this 
question.  In  the  compound  C  HI  the  carbon  is  supposed  to 
carry  a  charge  of  —  4,  and  in  C  O  (if  the  oxygen  is  tetra- 
valent)  a  charge  of  +  4 ;  the  value  of  a  for  C  H±  is  '0379,  and 
that  for  C  0  is  less,  viz.,  '0284,  although  the  residual  attrac- 
tion of  oxygen  is  probably  greater  than  that  of  hydrogen. 
This,  as  far  as  it  goes,  is  in  favour  of  the  view  that  the 
residual  attraction  of  carbon  is  greater  when  it  is  negatively 
than  when  it  is  positively  charged. 

Besides  affecting  the  relation  between  the  pressure  and 
volume,  the  residual  attraction  has  apparently  a  great  effect 
upon  the  specific  inductive  capacity  of  the  substance.  Thus, 
for  example,  the  liquids  which  contain  the  radicles  0  H, 
N  02,  C  O  H,  have  generally  very  large  specific  inductive 
capacities ;  and  moreover,  as  Drude  has  shown,  frequently 
show  anomalous  dispersion  for  electric  waves  whose  wave 
lengths  are  enormously  greater  than  the  size  of  a  molecule ; 
this  suggests  that  the  large  residual  attraction  between 
the  molecules  leads  to  the  formation  of  aggregates  con- 
taining a  very  large  number  of  molecules,  and  that 
the  exceptionally  large  value  of  the  specific  inductive 


138  THE  COKPUSCULAK  THEOKY  OF  MATTER. 

capacity  is  due  to  the  presence  in  these  liquids  of   such 
aggregates. 

On  the  view  of  chemical  combination  given  above,  the 
valency  of  an  element  depends  upon  the  number  of 
corpuscles  which  can  be  transferred  to  or  from  an  atom  of 
the  element  by  the  action  of  atoms  of  other  elements. 
For  each  valency  bond  established  between  two  atoms  the 
transference  of  one  corpuscle  from  the  one  atom  to  the 
other  has  taken  place,  the  atom  receiving  the  corpuscle 
acquiring  a  unit  charge  of  negative  electricity,  the  other 
by  the  loss  of  the  corpuscle  acquiring  a  unit  charge  of 
positive.  This  electrical  process  may  be  represented  by 
the  production  of  a  unit  tube  of  electric  force  between  the 
two  atoms,  the  tube  starting  from  the  positive  and  ending 
on  the  negative  atom.  In  this  way  we  can  give  a  physical 
interpretation  to  the  lines  by  which  in  graphical  formula} 
the  chemists  represent  the  valency  bonds,  these  lines 
representing  the  tubes  of  force  which  stretch  between  the 
atoms  connected  by  the  bond.  Thus,  for  example,  the  lines 
in  the  graphical  formula — 


represent  the  tubes  of  electric  force  which  stretch  between 
the  carbon  atom  and  the  four  hydrogen  atoms.  There  is, 
however,  one  important  difference  between  the  lines  repre- 
senting the  bonds  and  the  tubes  of  electric  force.  The 
lines  used  by  the  chemist  are  not  supposed  to  have  direc- 
tion. Thus,  in  the  two  compounds  — 


the  lines  joining  the  carbon  atom  to  the  hydrogen  atom  are 
not   distinguished    in    any   way    from    those    joining   the 


ARRANGEMENT   OF   CORPUSCLES   IN   ATOM.     139 

carbon  to  the  chlorine  atoms.  On  the  electrical  theory, 
however,  the  tubes  of  electric  force  are  regarded  as  having 
direction  starting  from  the  positive  and  ending  on  the 
negative  atom ;  thus,  if  the  hydrogen  atoms  are  positively 
electrified  in  marsh  gas  and  the  chlorine  atoms  negatively 
electrified  in  carbon  tetrachloride,  the  graphical  formulae 
representing  them  would  be — 


H  M  Cl 


respectively,  indicating  that  the  carbon  atom  is  not  in  the 
same  condition  in  the  two  compounds,  as  in  one  case  it  is 
the  terminus,  in  the  other  the  origin  of  the  tubes  of  electric 
force. 

A  method  of  investigating  the  magnitude  and  nature  of 
the  residual  attraction  exerted  by  a  gas  which  seems  not 
unlikely  to  lead  to  interesting  results,  is  to  find  the  effect 
produced  on  the  velocity  of  the  ions,  positive  as  well  as 
negative,  through  air  when  a  small  quantity  of  the  gas  under 
consideration  is  mixed  with  the  air.  Thus,  to  take  an 
example  of  the  effect  we  are  considering,  it  has  been  found 
that  in  carefully  dried  gases  the  velocity  of  the  negative  ion 
is  considerably  greater  than  that  of  the  positive  when  the 
electric  forces  acting  on  them  are  equal.  If,  however,  a 
little  water  vapour  is  added  to  the  gas  it  produces  a  con- 
siderable diminution  in  the  velocity  of  the  negative  ion 
while  it  hardly  affects  that  of  the  positive.  It  seems  quite 
possible  that  this  is  due  to  the  residual  attraction  of  the  OH 
radicle  in  the  water  for  a  negative  charge,  making  the  water 
molecules  attract  the  negative  ions  more  strongly  than 
they  do  the  positive  ones,  so  that  the  water  molecules  will 
tend  to  attach  themselves  to  the  negative  ions,  and  by 
loading  them  up  diminish  their  velocity.  It  would  be 
interesting  to  test  this  result  by  seeing  whether  other  gases 
which  contain  the  hydroxyl  group  OH  possess,  like  water, 


140  THE  COBPUSCULAK  THEORY  OF  MATTER. 

the  power  of  loading  up  negative  ions  to  a  greater  extent 
than  they  do  positive  ones ;  whether  also  there  are  not  other 
radicles  or  atoms  which  give  to  the  compounds  in  which 
they  occur  the  same  property ;  and  whether,  though  as  yet 
undiscovered,  there  may  not  be  other  atoms  or  radicles 
which  possess  the  power  of  loading  up  the  positive  ion  more 
than  the  negative  one. 

Another  property  which  may  perhaps  throw  light  on  the 
different  states  of  the  two  atoms  in  an  elementary  gas  is 
the  magnetic  qualities  possessed  by  some  elements  even 
when  in  the  gaseous  state.  Perhaps  one  of  the  most 
interesting  things  in  physics  is  the  magnetic  quality  of 
oxygen.  This  gas  when  in  the  molecular  condition  is 
strongly  magnetic ;  and  ozone  is  even  more  magnetic  than 
oxygen.  Oxygen  is  so  magnetic  that  liquid  oxygen  will  fly 
to  the  poles  of  a  bar  magnet  placed  near  it.  But  although 
oxygen  is  so  magnetic  in  the  molecular  condition,  it  does 
not,  with  few  exceptions,  of  which  the  most  noticeable  is 
nitric  oxide  (N  0),  preserve  this  quality  in  its  compounds. 
Thus  a  mixture  of  hydrogen  and  oxygen  in  the  proportion 
of  two  volumes  of  hydrogen  to  one  of  oxygen  is  magnetic, 
but  if  the  hydrogen  and  oxygen,  instead  of  being  mechani- 
cally mixed,  enter  into  chemical  combination  and  form 
water  vapour,  the  result  is  a  diamagnetic  substance.  Again, 
equal  volumes  of  oxygen  and  carbonic  acid  gas  contain  the 
same  amount  of  oxygen,  yet  the  oxygen  is  magnetic,  the 
carbonic  acid  diamagnetic. 

I  am  inclined  to  think  that  this  property  of  oxygen  is  due 
to  one  of  the  atoms  in  a  molecule  of  oxygen  being  in  a  state 
in  which  the  atom  is  not  usually  found  in  oxygen  com- 
pounds, and  that  it  is  to  the  atoms  in  this  state  that 
oxygen  owes  its  magnetic  quality.  If  we  suppose  that  the 
two  atoms  in  the  molecule  of  oxygen  are  held  together  by 
electrical  forces,  one  atom  being  positively,  the  other 
negatively  electrified,  then  in  the  molecule  of  oxygen  we 
have  a  positively  electrified  atom  of  oxygen,  i.e.,  an  atom 
which  has  lost  at  least  one,  and  probably  more  than  one, 
corpuscle,  while  in  at  any  rate  the  vast  majority  of  oxygen 


ARRANGEMENT   OF   CORPUSCLES   IN   ATOM.     141 

compounds  the  oxygen  atom  is  negatively  electrified.  Now,  if 
we  suppose  that  the  oxygen  atom  which  has  lost  corpuscles — 
i.e.,  the  positively  electrified  one — is  magnetic,  while  the  one 
which  has  gained  them — i.e.,  the  negatively  electrified  atom — 
is  either  non-magnetic  or  diamagnetic,  we  can  evidently 
easily  account  for  oxygen  being  magnetic  in  O2,  and  non- 
magnetic or  diamagnetic  in  its  compounds.  In  support  of 
this  view  we  may  urge  that  a  similar  phenomenon  seems 
to  occur  in  the  case  of  iron,  for  Townsend  has  shown 
that  in  solutions  of  iron  salts  the  magnetic  qualities  of 
the  iron  depend  greatly  upon  the  nature  of  the  salts:  thus  for 
all  ferric  salts  the  coefficient  of  magnetisation  is  equal  to  aN 
where  N  is  the  number  of  atoms  of  iron  in  unit  volume  of  the 
solution,  and  a  is  a  constant  which  does  not  depend  upon 
the  element  with  which  the  iron  is  in  combination.  Again, 
the  coefficient  of  magnetisation  of  all  ferrous  salts  is  ft  N, 
where  ft  is  again  independent  of  the  other  constituent  of  the 
salt ;  /3  is  not  the  same  as  a ;  both  the  ferrous  and  ferric 
salts  are  strongly  magnetic,  and  in  them  it  will  be  noticed 
that  the  iron  atom  is  positively  charged.  When,  however, 
the  iron  atom  occurs  in  the  negative  part  of  the  molecule, 
as  in  the  ferricyanides,  Townsend  proved  that  it  showed 
no  magnetic  quality,  the  ferricyanides  being  no  more 
magnetic  than  salts  not  containing  iron.  This  shows  that 
the  iron  atom  may  be  magnetic  or  non-magnetic  according 
as  it  is  on  the  positively  or  negatively  electrified  side  of  the 
molecule;  and  the  phenomena  associated  with  the  magnetism 
of  oxygen  and  its  compounds  indicate  that  the  oxygen  atom 
possesses  a  similar  property. 


CHAPTEK  YIL 

ON    THE    NUMBER    OF    CORPUSCLES    IN    AN    ATOM. 

IF  we  take  the  view  that  corpuscles  are  an  essential 
constituent  of  the  atom,  one  of  the  most  fundamental 
questions  to  be  answered  is,  how  many  corpuscles  are 
there  in  an  atom  ? 

We  shall  consider  three  methods  by  which  an  estimate 
of  the  number  of  corpuscles  in  an  atom  may  be  obtained. 

METHOD  I. — SECONDARY  RONTGEN  RADIATION. 

This  method  is  based  on  the  determination  of  the  pro- 
portion between  the  energy  in  a  beam  of  primary  Rontgen 
rays  passing  through  a  gas  and  that  in  the  secondary  Rontgen 
rays  emitted  by  the  gas  through  which  the  primary  rays 
are  passing. 

When  an  electrified  body  is  suddenly  set  in  motion,  or  if 
when  in  rapid  motion  it  is  suddenly  stopped,  pulses  of  intense 
electric  and  magnetic  force  start  from  the  body  and  travel 
outwards  through  space  with  the  velocity  of  light.  The 
pulses  produced  when  the  rapidly  moving  electrified  particles 
in  a  vacuum  tube,  called  cathode  rays,  strike  against  the  walls 
of  the  tube  and  have  their  velocities  rapidly  diminished, 
constitute  on  our  hypothesis  the  well-known  Rontgen  rays. 
We  regard,  then,  the  Rontgen  rays  as  very  thin  pulses  of 
intense  electric  and  magnetic  force.  When  such  a  pulse 
strikes  against  a  corpuscle  the  electric  force  in  the  pulse 
acting  on  the  electric  charge  on  the  corpuscle  in  a  very 
short  time  makes  the  corpuscle  move  with  a  great  velocity. 
This  sudden  starting  of  the  electrified  corpuscle  produces 
another  pulse  of  electric  and  magnetic  force,  and  the  aggre- 
gate of  such  pulses  constitutes  the  secondary  radiation 


NUMBER   OF   CORPUSCLES   IN   AN   ATOM.     143 

emitted  by  the  substance  containing  the  corpuscles.  The 
corpuscle  will  emit  the  pulse  only  while  the  velocity  is 
changing,  and  if  the  corpuscle  is  free,  or  if  the  other  forces 
acting  upon  it  are  small  compared  with  those  in  the  pulse 
of  primary  Rontgen  radiation,  the  change  in  the  velocity 
of  the  corpuscle  will  take  place  while,  and  only  while,  the 
primary  pulse  is  passing  over  it,  and  the  thickness  of  the 
secondary  pulse  will  be  the  same  as  that  of  the  primary ;  in 
this  case  the  quality  of  the  secondary  radiation  as  measured 
by  its  penetrating  power  will  be  the  same  as  that  of  the 
primary.  If,  however,  the  corpuscle,  after  being  displaced 
by  the  primary  ray,  is  acted  upon  by  very  intense  forces 
due  to  the  proximity  of  other  corpuscles,  it  is  evident  that 
the  character  of  the  secondary  pulse  will  not  be  the  same 
as  when  those  forces  are  small,  for  in  the  latter  case  the 
acceleration  of  the  corpuscle  will  sink  to  a  very  small  value 
as  soon  as  the  primary  pulse  has  left  the  corpuscle,  so 
that  the  primary  and  secondary  pulses  will  have  the  same 
thickness,  while  in  the  former  case  the  acceleration  of  the 
corpuscle  will  be  large  long  after  the  pulse  has  passed  the 
corpuscle ;  thus  the  breadth  of  the  secondary  pulse  will  be 
much  increased,  and  the  secondary  radiation  will  be  of  a 
much  more  absorbable  type  than  the  primary.  Again,  if 
the  primary  pulse  is  so  thick  or  the  corpuscles  are  so  closely 
packed  that  before  the  pulse  has  left  one  corpuscle  it  over- 
laps another,  the  pulses  emitted  by  the  corpuscles  will  not 
be  separated  by  a  finite  interval,  but  will  overlap  and  produce 
a  pulse  thicker  than  the  primary  one.  Thus  if  we  find  that 
the  secondary  radiation  is  of  the  same  type  as  the  primary, 
we  may  conclude  that  the  pulses  are  so  thin  that  they  act 
upon  the  corpuscles  one  at  a  time,  and  also  that  the  forces 
of  restitution  called  into  play  by  the  displacement  of  the 
corpuscle  are  small  compared  witli  the  forces  exerted  on  the 
corpuscle  by  the  electric  force  in  the  primary  pulse.  When  these 
conditions  are  fulfilled  it  can  be  shown  (see  J.  J.  Thomson, 
"  Conduction  of  Electricity  through  Gases,"  2nd  edition, 
p.  326)  that  the  energy  of  the  secondary  radiation  emitted 
per  unit  time  per  unit  volume  of  a  space  containing  corpuscles 


144  THE  CORPUSCULAK  THEORY  OF  MATTER. 

,  ,    8  TT  N  e4  .  .  .     .  , 

is  equal  to  —  —  ^  times  the  energy  in  the  primary  radiation 

passing  through  unit  volume  in  that  time.  N  is  the  number 
of  corpuscles  per  unit  volume,  e  the  charge  on  a  corpuscle, 
and  m  its  mass. 

Now  Barlda,  who  has  made  very  valuable  investigations 
on  the  Secondary  Radiation  produced  by  Rontgen  rays, 
finds  that  for  elements  with  small  atomic  weight  the 
quality  of  the  secondary  radiation  is  the  same  as  that  of 
the  primary.  He  finds,  too,  in  accordance  with  the  expres- 
sion just  found,  that  the  proportion  between  the  energy  of 
the  secondary  radiation  from  such  elements  and  the  primary 
radiation  is  independent  of  the  nature  of  the  primary  radia- 
tion, and  that  for  different  substances  this  ratio  is  directly 
proportional  to  the  density  of  the  substance.  Since  this 

ratio  is  equal  to  —      —^t  this  result  shows  that  the  number 

o       111" 

of  corpuscles  in  unit  volume  is  proportional  to  the  density 
of  the  substance,  and  since  the  density  is  equal  to  the 
number  of  atoms  per  unit  volume  multiplied  by  the  atomic 
weight,  it  follows  from  this  result  that  the  number  of 
corpuscles  in  an  atom  is  proportional  to  the  atomic  weight 
of  the  substance,  e.g.,  that  the  number  of  corpuscles  in  an 
atom  of  oxygen  is  sixteen  times  that  in  an  atom  of  hydrogen, 
and  so  on. 

Barkla  finds  that  the  energy  of  the  secondary  radiation 
from  one  cubic  centimetre  of  air  at  atmospheric  pressure  is 
about  '00025  that  of  the  primary  radiation  passing  through 
it.  Hence  we  have  — 


=  -00025. 
3     m2 

Now    e  =  1-2  x  10-20  and    e/ni  =  I'l  x  107.     Substituting 
these  values,  we  find  — 

Ne  =  10. 

If  n  is  the  number  of  molecules  in  a  cubic  centimetre  of  air 
at  atmospheric  pressure  and  0°  C.  we  know— 

ne  =  *4. 


NUMBER  OF   COKPUSCLES  IN   AN   ATOM.     145 

Thus  JV  =  25??,  so  that  the  molecules  of  air  contain  on  the 
average  about  twenty-five  corpuscles.  The  molecular 
weight  of  nitrogen  is  28 ;  this  result  suggests  that  the 
number  of  corpuscles  in  the  atom  of  nitrogen  is  equal  to 
the  atomic  weight  of  nitrogen.  Since  the  energy  scattered 
by  different  gases  is  proportional  to  the  density  of  the  gas, 
the  number  of  corpuscles  per  unit  volume  must  be  also 
proportional  to  the  density ;  hence  if  the  number  of 
corpuscles  in  an  atom  of  any  one  substance  is  equal  to 
the  atomic  weight  of  that  substance,  the  number  in  an  atom 
of  any  substance  whatever  must  be  equal  to  the  atomic 
weight  of  that  substance. 

As  this  is  a  question  of  very  great  importance  it  is  neces- 
sary to  consider  carefully  the  assumptions  made  in  proving 

that  the  energy  radiated  per  unit  volume  is  equal  to  -=-  — g- 

times  the  energy  in  the  primary  rays.  N  is  the  number 
of  corpuscles  set  in  motion  by  the  primary  pulse  ;  we  have 
assumed  that  all  the  corpuscles  are  set  in  motion.  It  might 
be  that  some  of  the  corpuscles  are  bound  to  the  sphere  of 
positive  electrification  by  forces  so  strong  that  practically 
the  corpuscles  are  rigidly  attached  to  the  atom  and  can- 
not move  without  dragging  the  whole  atom  with  them  ;  the 
acceleration  of  corpuscles  such  as  these  would  be  so  small 
that  they  would  give  rise  to  very  little  radiation  in  com- 
parison with  the  freely  moving  corpuscles,  so  that  any 
method  based  on  secondary  radiation  would  not  be  able  to 
detect  these  fixed  corpuscles.  We  shall  see,  however,  that 
such  could  be  detected  by  our  second  method. 

Another  assumption  made  was  that  the  pulse  of  Eontgen 
radiation  was  so  thin  as  not  to  contain  more  than  one  cor- 
puscle at  once.  In  favour  of  this  is  the  fact  that  the  secondary 
radiation  from  light  substances  is  of  the  same  quality  as 
the  primary,  whereas  if  the  pulse  covered  several  corpuscles 
at  once,  the  thickness  of  the  pulse  of  the  secondary  radiation 
would  be  greater  than  that  of  the  primary  pulse  by  the 
distance  between  two  corpuscles  if  the  pulse  at  each  collision 
passed  over  two  corpuscles  before  it  got  free  from  a  corpuscle, 

T.M.  L 


146  THE  CORPUSCULAR  THEORY  OF  MATTER. 

by  twice  this  distance  if  it  passed  over  three,  and  so  on.  This 
would  make  a  great  difference  in  the  quality  of  the  secondary 
radiation  if  the  thickness  of  the  primary  pulse  were  only 
a  small  multiple  of  the  distance  between  two  corpuscles.  It 
would  make  comparatively  little  difference  if  the  thickness 
of  the  pulse  were  much  greater  than  the  diameter  of  an 
atom;  so  that  the  identity  of  the  secondary  and  primary 
radiation  is  not  inconsistent  with  very  thick  pulses,  although 
it  is  so  with  moderately  thick  ones.  If  the  pulses  are 
thicker  than  the  atom,  then  all  the  corpuscles  in  an  atom 
will  be  moving  as  if  they  were  a  single  charged  body,  with 
a  charge  p  e,  and  a  mass  p  m  if  p  is  the  number  of 
corpuscles  in  the  atom;  hence  the  energy  radiated 

per  atom  will  be  -^-  — ?-',  if  n  is  the  number  of  atoms 
o       m 

per  unit  volume,  the  energy  radiated  per  unit  volume  is 

o  n  p2.      Since  experiment   shows   that    this   is   pro- 
3   m2 

portional  to  the  density,  i.e.,  to  n  M  if  M  is  the  atomic 
weight,  we  see  that  if  the  Rontgen  radiation  were  of  this 
character  p2  would  be  proportional  to  M,  so  that  p,  the 
number  of  corpuscles  in  the  atom,  would  be  proportional 
to  the  square  root  of  the  atomic  weight. 

The  fact  that  the  secondary  radiation  from  light  liquids 
and  solids,  as  well  as  of  gases,  is  of  the  same  character  as 
that  of  the  primary,  shows,  however,  that  the  pulses  in  the 
primary  radiation  cannot  be  so  thick  as  we  have  supposed, 
for  if  the  thickness  of  the  pulse  were  much  greater  than  the 
diameter  of  an  atom  then  such  a  pulse  on  passing  through 
a  solid  or  liquid  consisting  of  such  atoms  would  never  be 
free  from  corpuscles,  and  the  secondary  pulse  would  be  very 
much  thicker  and  more  drawn  out  than  the  primary. 

When  the  primary  pulse  is  thicker  than  the  atom  and 
the  electric  force  is  in  the  same  direction  from  back  to  front, 
the  energy  radiated  per  atom  is  proportional  to  the  square 
of  the  number  of  corpuscles  in  the  atom  instead  of  to  the 
first  power  of  the  number,  as  it  is  when  the  pulses  are 
thin ;  thus  the  radiation  increases  more  rapidly  with  the 


NUMBER   OF   CORPUSCLES   IN   AN   ATOM.     147 

number  of  corpuscles  for  thick  pulses  of  this  type  than 
for  thin  ones.  This,  however,  is  only  true  when  the 
electric  force  is  uniform  in  direction  throughout  the  pulse. 
When  the  electric  force  in  the  pulse,  instead  of  being 
uniformly  in  one  direction,  is  in  one  direction  in  the  front 
of  the  pulse  and  in  the  opposite  direction  in  the  rear, 
the  radiation  from  a  thick  pulse  will  be  less  than  from 
a  thin  one,  for  the  corpuscles  in  the  rear  of  the  thick  pulse 
will  have  opposite  accelerations  to  those  in  the  front ;  the 
electric  and  magnetic  forces  produced  by  them  will  be  in 
opposite  directions,  they  will  neutralise  each  other's 
effects,  and  the  radiation  from  the  two  combined  will  be 
much  less  than  from  either  individually.  On  the  other 
hand,  when  the  pulse  is  so  thin  that  it  can  only  cover  one 
corpuscle  at  a  time  the  radiation  from  each  corpuscle  will 
spread  out  independently  and  the  energy  radiated  will  be 
directly  proportional  to  the  number  of  corpuscles. 

The  secondary  radiation  from  substances  with  large  atomic 
weights  is  not  entirely  of  the  same  character  as  the  primary 
radiation,  indeed,  from  these  substances  by  far  the  greater 
part  of  the  secondary  radiation  consists  of  cathode  rays  of 
an  easily  absorbable  type,  so  that  as  a  whole  the  secondary 
radiation  is  very  much  less  penetrating  than  the  primary. 
Barkla  found  that  the  amount  of  secondary  radiation  of  the 
same  penetrating  type  as  the  primary  produced  by  sub- 
stances with  large  atomic  weights  is  often  less  than  that 
from  the  lighter  elements ;  in  the  case  of  the  latter,  however, 
practically  all  the  secondary  radiation  is  of  a  penetrating 
type,  while  this  type  forms  only  a  fraction  of  the  total 
radiation  from  the  heavier  elements.  We  should  expect 
the  penetrating  radiation  to  begin  to  diminish  if  the  cor- 
puscles in  the  atom  get  so  crowded  that  the  Rontgen  pulses 
spread  over  more  than  one  corpuscle  at  once,  provided  that  the 
direction  of  the  electric  force  in  the  pulse  is  reversed  between 
the  front  and  the  rear  of  the  pulse.  Barkla  found  that  with 
the  rays  he  used,  the  elements  of  smaller  atomic  weight 
than  calcium  gave  off  secondary  radiation  of  the  same  type 
as  the  primary,  while  the  secondary  radiation  from  calcium 

L  2 


148  THE  CORPUSCULAR  THEORY  OF  MATTER. 

and  elements  with  larger  atomic  weights  consisted  chiefly 
of  easily  absorbable  cathode  rays.  I  found  that  the  element 
at  which  the  change  took  place  depended  upon  the  quality 
of  the  primary  rays,  and  that  with  very  soft  rays  the 
change  in  the  character  of  the  secondary  radiation  can  take 
place  at  lighter  elements  than  calcium. 

If,  as  the  result  of  the  passage  of  the  primary  rays 
through  the  gas,  the  gas  is  ionized,  i.e.,  if  corpuscles  are 
detached  from  the  atoms,  the  collisions  made  by  these 
corpuscles  will  increase  the  secondary  radiation ;  this 
increase  will,  however,  consist  of  a  radiation  which  is  not 
in  general  of  the  same  type  as  the  primary. 

SECOND  METHOD  OF  ESTIMATING  THE  NUMBER  OF  CORPUSCLES 
IN  AN  ATOM  :  BY  DETERMINING  THE  OPACITY  OF  A  SUB- 
STANCE TO  CATHODE  RAYS. 

If  a  cathode  ray  is  travelling  with  a  very  high  velocity 
through  a  collection  of  corpuscles,  then  when  it  passes  close 
to  one  of  the  corpuscles  it  will  be  deflected ;  as  the  result  of 
such  deflections  a  bundle  of  cathode  rays  originally  parallel  to 
the  axis  of  x  will  get  more  and  more  diffuse  as  they  pass  through 
the  substance,  and  the  number  passing  in  unit  time  through  a 
unit  area  at  right  angles  to  the  axis  of  x  will  get  smaller  and 
smaller  as  the  length  of  path  of  the  rays  increases.  The 
amount  of  deflection  experienced  by  the  moving  corpuscle  will 
depend  to  some  extent  upon  the  firmness  with  which  the  cor- 
puscles in  the  absorbing  substance  are  held  in  their  positions 
of  equilibrium  by  the  forces  inside  the  atom.  The  solution  of 
the  problem  when  these  forces  are  taken  into  account  would 
be  exceedingly  difficult  and  complex.  We  may,  however, 
represent  to  some  extent  the  action  of  these  forces  by 
increasing  the  mass  of  the  corpuscles  in  the  absorbing  sub- 
stance, the  effect  of  a  corpuscle  that  is  held  absolutely 
rigidly  by  the  forces  acting  upon  it  being  the  same  as  if  it 
were  free  from  such  forces  but  had  an  infinite  mass. 

It  can  be  shown  that  on  these  suppositions  the  number  of 
corpuscles  which  pass  through  unit  area  at  right  angles  to 
the  x  axis,  at  a  distance  x  from  the  place  where  the  stream  of 


NUMBEK   OF   CORPUSCLES   IN   AN   ATOM.    149 

corpuscles  enters  the  substance,  is  equal  to  70  e~Aa;,  where 
TO  is  the  number  when  x  =  o  and  — 


FpV  Mx  +  M.  ,       /a  /ryjf.M.     _  XN 

K/     MiMf     D  W'W^  +  Mg      r 


(See  J.  J.  Thomson,  P/«7.  A%.,  June,  1906,  "  Conduction 
of  Electricity  through  Gases,"  2nd  edition,  p.  377.) 

In  this  expression  N  is  the  number  of  corpuscles  per  unit 
volume  of  the  absorbing  substance,  e  the  charge  on  a 
corpuscle  in  electro-magnetic  units,  MI  the  mass  of  a 
corpuscle  in  the  atoms  of  the  absorbing  substance,  M2 
that  of  the  moving  corpuscle,  V  the  velocity  of  the  moving 
corpuscle,  F0  the  velocity  of  light,  and  a  the  distance  between 
the  corpuscles  in  the  atoms  of  the  absorbing  substance  ;  X  is 
the  coefficient  of  absorption  of  the  cathode  rays  in  the  sub- 
stance. We  can  express  the  value  of  A.  in  terms  of  P,  the 
number  of  corpuscles  in  an  atom  of  the  absorbing  substance, 
for  if  d  is  the  density  of  the  substance,  /x  the  mass  of  an 
atom,  P  d  =  NP,  thus— 


Now  e/M,  =  1-7  X  107 
e  =  1-2  X  ID'20 

-  =  104  Iw,  where  w  is  the  atomic  weight  of  the 
H- 

absorbing   substance,  and  r0  =  3  X  1010  is   the  velocity 
of  light. 

Substituting  these  values  we  find  — 

*  _.  47rP  Fo*      H)5  M1  +  M2         /a    V 

" 


"     w    v*  "  so 


/a  (V  \*M±xM*  _  -\ 

\f\vj  afi+Mt 


The  absorption  considered  in  this  investigation  is  that  due 
to  the  scattering  of  the  corpuscles  by  collisions  with  other 
corpuscles  ;  the  change  in  the  kinetic  energy  of  the  colliding 
corpuscle  is  neglected.  This  absorption  is  analogous  to  the 


150  THE  CORPUSCULAR  THEORY  OF  MATTER. 

scattering  which  takes  place  when  a  ray  of  light  passes 
through  a  layer  of  powdered  glass.  As  it  is  important  to 
have  a  clear  idea  of  what  is  meant  by  this  coefficient  we 
shall  consider  a  special  case.  Suppose  the  incident 
corpuscles  form  a  thin  cylindrical  beam  E  F  G  H;  after 
passing  through  the  absorbing  substance  this  beam  will  be 
scattered,  and  its  section  will  be  much  larger.  The  coefficient 
of  absorption  we  have  investigated  is  measured  by  the 
diminution  in  the  energy  passing  across  a  section  of 
L  M  N  P,  the  prolongation  of  the  incident  beam,  and  not 
to  the  diminution  in  the  total  amount  of  energy  passing 
through  the  plate ;  this  will  of  course  be  much  less  than  the 
diminution  in  the  energy  passing  through  a  section  of 
L  M  N  P.  Thus  if  the  corpuscles  originate  from  a  radio- 
active substance  placed  in  a  metal  tube  E  F  G  H,  the 
coefficient  of  absorption  of  the  plate  is  measured  by  the 
diminution  in  the  number  which  pass  through  a  tube 
L  M  N  P,  the  prologation  of  the  tube  in  which  the  radio- 
active substance  is  placed,  and  not  by  the  diminution  in 
the  number  of  corpuscles  which  find  their  way  through  the 
plate.  In  the  experiments  hitherto  made  on  the  absorption 
of  the  /3  rays  the  quantity  measured  has  been  the  ionisation 
produced  by  all  the  rays  which  emerge  from  the  absorbing 
layer ;  this  may  explain  the  reason  why  the  values  of  \/d 
obtained  by  various  physicists  for  the  ft  rays  given  out  by 
radio-active  substances  are  much  smaller  than  the  values  for 
rapidly-moving  cathode  rays  produced  in  a  vacuum  tube, 
when  the  absorptions  have  been  determined  by  measuring 
the  quantity  passing  through  a  constant  area,  like  that  of 
the  section  of  the  tube  L  M  N  P,  and  not  the  quantity 
passing  through  the  whole  of  the  absorbing  plate.  That 
this  difference  is  very  marked  and  too  great  to  be  accounted 
for  by  differences  in  the  velocities  of  the  corpuscles  may  be 
seen  from  the  fact  that  \/d  varies  from  5  to  10,  for  the  p 
rays  from  uranium,  which,  according  to  Becquerel,  have  a 
velocity  of  T6  X  1010  cm/sec.,  while  Becker  found  that  for 
cathode  rays  with  a  velocity  of  1010  cm/sec.  \/d  varied 
between  1,200  and  2,000.  Some  experiments  recently 


NUMBER  OF   CORPUSCLES   IN  Atf  ATOM.     151 

made  at  the  Cavendish  Laboratory  by  Mr.  Crowther  have 
shown  that  when  A  is  the  diminution  in  the  quantity  of 
rays  passing  through  unit  area  Xfd  for  rays  from 
uranium  is  as  much  as  150.  As  the  quantity  measured 
in  the  experiment  with  the  cathode  rays  corresponds  to  our 
coefficient  of  absorption,  while  that  for  the  uranium  rays 
does  not,  we  shall  use  the  former  to  determine  the  value 
of  P/w. 

Taking  the  case  investigated  by  Becker,  where  V  =  1010, 
and  putting  MI  =  Ma,  we  find  from  the  equation  on  page 
149  that— 


But    (sec    p.   34)    M  =  f  ~  where  6  =  1CT18  and  is  the 

3  o 

radius  of  a  corpuscle,  hence  — 

X        c_  P  ,        /          a 

-d  =  67  ,7  log'  (27  x  10-"  ~ 

if  we  take  a  to  be  of  the  order  10~8 


approximately—  _  -K^  P 

w 

As  \/d  varies  between  1,200  and  2,000,  we  see  from  this 
that  P/w  cannot  be  large,  i.e.,  that  the  number  of  corpuscles 
in  the  atom  must  be  of  the  same  order  as  the  atomic 
weight. 

This  method  supplements  the  preceding  method  (p.  142), 
for  on  the  former  method  corpuscles  which  are  so  firmly 
held  that  they  are  not  moved  by  the  Rontgen  rays  would 
not  be  accounted  for.  The  present  method  is  not  open  to 
this  objection ;  on  the  other  hand,  this  method  involves  the 
assumption  that,  however  small  may  be  the  distance 
between  the  corpuscles,  the  repulsion  between  them  varies 
inversely  as  the  square  of  the  distance. 


152  THE  CORPUSCULAR  THEORY  OF  MATTER. 

THE   INFORMATION   GIVEN   BY   THE  OPTICAL  PROPERTIES  OF 
BODIES  ON  THE  STRUCTURE  OF  THE  ATOM. 

We  could  estimate  the  number  of  corpuscles  if  we  had 
measurements  of  the  dispersion  of  light  by  a  monatomic  gas. 
For  it  can  be  shown  (see  Phil.  Mag.,  June,  1906)  that  if  the 
atom  contains  n  corpuscles  in  a  sphere  of  uniform  positive 
electrification,  the  refractive  index  ^  of  the  gas  for  light 
waves  with  a  frequency  p  is  given  by  the  equation — 

1$  -  1  _  _  |  TT  N  (m  E2  +  M  E  e) (1) 

Ij?  +  2  =  :  J  TT  p  (M  e  +  mE)  —  m  M  p* 

here  N  is  the  number  of  atoms  per  cubic  centimetre,  e  the 
charge  on  a  corpuscle  whose  mass  is  m,  M  the  mass  of  the 
sphere  of  positive  electrification,  E  the  magnitude  of  the 
positive  charge,  so  that  E  =  n  e,  p  is  the  density  of 
the  positive  electricity.  The  waves  of  light  are  supposed 
to  be  vfery  much  longer  than  the  diameter  of  an  atom,  so 
that  the  electric  force  in  the  light  wave  is  regarded  as 
constant  throughout  an  atom. 

For  infinitely  long  waves  p  =  o,  hence 

=  N  (volume  of  the  sphere  of  positive  electrification). 

=  volume  occupied  by  these  spheres  per  cubic  centimetre 
of  the  gas. 

This  value  agrees  with  that  given  by  Mossotti's  theory, 
where  the  atoms  are  regarded  as  perfectly  conducting 
spheres. 

If  the  term  in  p2  is  small,  Equation  (1)  may  be  written — 

•'2  -  1       N  E    \  ,    ,Mm     3E          1 

-4-    .    ii~  '). 

'       TVT    •  A  -i  /r     i  r     \ 


^2  +  2          p 

=  N  E    1  1  4.  ^     BE  M  2) 

P        \  e2  '  4  TT  p  '  n  (M  +  n  in)  P  f 

the  only  factor  which  involves  n  is     /7l/ri. r  and  this  is 

n  (M  -f  n  m) 

always  less  than  1/n,  thus  the  dispersion  (for  the  same  sized 


NUMBER  OF   CORPUSCLES   IN  AN  ATOM.    153 

atom)  will  diminish  rapidly  as  n  increases,  and  by  measure- 
ments of  the  dispersion  we  could  get  an  estimate  of  the  value 
of  n.  Though  we  have  at  present  no  measurements  of  the 
dispersion  of  the  monatomic  gases,  there  seems  reason 
from  some  experiments  made  by  Lord  Rayleigh  to  believe 
that  it  is  of  the  same  order  as  for  diatomic  gases.  The 
dispersion  of  hydrogen  has  been  shown  by  Ketteler  to  be 
given  by  the  formula — 

/x2  —  1  _  1  /  2-8014  X  1CT4  +  2  X  10~14_1  \ 

/x2  +  2  ~~  3  \  T2J 

where  A.  is  the  wave  length. 
Comparing  this  with  the  above  formula,  and  remembering 

2   7T    V 

that  p  =  — - —  where  V  is  the  velocity  of  light,  we  find — 

A, 

1         M 

=  1  approximately. 


n  M  -f-  n  m 

This  result  shows  that  n  cannot  differ  much  from  unity, 
hence  if  a  monatomic  gas  had  the  same  density  and  the 
same  optical  properties  as  hydrogen,  it  could  not  have  many 
corpuscles  in  the  atom.  This  result  confirms  those  given 
by  the  preceding  methods,  that  the  number  of  corpuscles 
in  the  atom  is  proportional  to  the  atomic  weight. 

The  preceding  expression  for  the  refractive  index  of  a 
gas  involves  the  assumption  that  the  force  exerted  by  the 
positive  electricity  tending  to  bring  a  corpuscle  back  to  its 
original  position  when  displaced  is  equal  to  /*  times  the 
displacement  where  /*  is  the  same  for  all  the  corpuscles. 
This  assumption,  however,  is  not  true  for  diatomic  mole- 
cules where  the  atoms  are  held  together  by  the  forces 
resulting  from  the  displacement  of  the  valency  corpuscles. 
Thus,  to  take  a  simple  case,  when  we  have  two  atoms  each 
containing  one  corpuscle,  the  atoms  being  of  different  sizes, 
when  the  smaller  atom  gets  a  certain  distance  inside  the 
larger  one,  the  corpuscle  which  was  originally  at  the  centre 
of  the  larger  atom  suddenly  jumps  into  the  smaller  one  and 
takes  up  a  position  at  E  inside  the  smaller  atom,  E  being 
on  the  same  side  of  13,  the  centre  of  the  smaller  atom,  as  A 


154  THE  CORPUSCULAR  THEORY  OF  MATTER. 

the  centre  of  the  larger  one.  The  corpuscle  which  was 
originally  at  B  is  displaced  to  F,  F  and  E  being  on 
opposite  sides  of  B.  The  corpuscle  at  E  corresponds  to  the 
valency  corpuscle. 

Consider  this  corpuscle  when  it  was  in  a  position  EI 
before  moving  into  the  smaller  atom  :  if  it  is  displaced 
through  a  distance  £,  the  forces  due  to  the  positive  electri- 
fication tending  to  bring  it  back  to  its  original  position  are 

/  e2        2  #2     \ 

\  ~3"~7y^     /^'  wn^e  ^  -^1  was  ^ne  corresponding  position 


of  F,  the  forces  tending  to  bring  it  back  are  (  -g  +  j~B  )  £,  where 

\a       u  / 

a  and  b  are  the  radii  of  the  larger  and  smaller  atoms  respec- 
tively. The  coefficients  of  £in  these  expressions  are  different, 
and  the  preceding  investigation  does  not  apply.  To  find  the 
expression  for  the  refractive  index  in  a  case  like  this  we 
may  make  use  of  a  theorem  due  to  Lorentz,  which  states 
that  the  refractive  index  /*  for  light  whose  frequency  isp,  due 
to  a  system  of  electrified  particles  with  a  charge  e  and 
mass  in,  and  having  pi9  p^  p3,  .  .  .  for  the  frequencies  of 
their  vibrations  about  their  positions  of  equilibrium,  is 
given  by  the  equation  — 

a 

?  —  1 


^2+  2 

where  NI  is  the  number  of  systems  per  unit  volume 
having  the  frequency  plt  N^  the  number  having  the 
frequency  p%,  and  so  on. 

It  follows  from  this  expression  that  the  systems  for 
which  pr  is  small  make  the  largest  contributions  to  the  value 
of  (/A2  —  l)/(/^2  +  2).  When  pr  is  small  the  force  of  restitution 
tending  to  bring  the  electrified  particle  back  to  its  original 
position  when  it  is  displaced  from  it,  is  small,  so  that  the 
particles  which  are  easily  displaced  are  those  which  have 
the  greatest  influence  on  the  refraction.  If  we  suppose  that 
there  are  some  particles  which  are  so  much  more  easily  dis- 
placed than  others  that  their  influence  on  the  refractive 
index  swamps  that  of  the  other  particles,  and  if  we  suppose 


NUMBER   OF   CORPUSCLES   IN   AN   ATOM.    155 

that  these  loosely  held  particles  have  all  the  same  period^, 
then  we  shall  have,  if  N  is  the  number  of  these  particles 
per  unit  volume — 


Now  there  is  a  number  of  substances  for  which  the 
relation  between  the  refractive  index  and  the  frequency 
can  be  expressed  by  the  simple  relation  — 

/x2  -  1  A 

f  +  2   J=  pf-p* 

and  the  experiments  of  Ketteler  and  others  furnish  us  with 
the  values  of  A.  Comparing  this  with  the  preceding 
expression  for  (^  —  1)  /  (//,2  +  2)  we  see  that— 

A  =  »* 


III 


Now  since  we  know  e/m  and  e,  we  can  from  this  equation 
determine  N,  tjie  number  of  these  systems  in  unit  volume. 
This  has  been  done  by  Drude,  who  finds  that  the  number 
determined  in  this  way  is  greater  than  the  number  of  atoms 
in  that  volume  but  not  very  much  greater  ;  it  is  very  seldom, 
for  example,  as  much  as  ten  times  greater.  Also  Drude  found 
that  the  greater  the  chemical  valency  of  the  atoms  in  the 
refracting  substance  the  greater  was  the  number  of  the 
refracting  systems  per  atom.  Since  in  substances  of  great 
atomic  weight  the  number  of  these  refracting  systems  is 
only  three  or  four  times  the  number  of  the  atoms,  and 
therefore  small  compared  with  the  number  of  corpuscles,  it 
is  evident  that  the  corpuscles  in  the  atom  do  not  all  take 
the  same  share  in  producing  refraction,  but  that  practically 
the  whole  of  the  work  is  done  by  a  small  fraction  of  the 
corpuscles,  and  that  the  greater  the  valency  the  larger  is  the 
number  of  corpuscles  which  give  rise  to  refraction.  We 
should  expect  a  result  of  this  kind,  for  the  valency  gives  an 
indication  of  the  number  of  corpuscles  displaced,  and  these 
corpuscles,  which  are  displaced  by  the  action  of  one  atom 


156  THE  CORPUSCULAR  THEORY  OF  MATTER. 

on  others,  are  in  all  probability  much  less  firmly  fixed  than 
those  which  retain  their  positions  under  this  action  ;  thus 
since  the  valency  corpuscles  are  the  ones  most  easily  moved 
they  are  the  ones  which  produce  the  greatest  effect  upon  the 
refractive  index.  The  optical  properties  of  other  than  mon- 
atomic  gases  are  thus  complicated  by  considerations  which 
make  them  unsuitable  for  determining  the  total  number  of 
corpuscles  in  the  atom. 

In  a  discussion  of  the  optical  properties  of  gases  we  must 
consider  a  very  obvious  objection  to  the  view  that  the  num- 
ber of  corpuscles  in  the  atom  is  not  a  large  multiple  of  the 
atomic  weight.  The  objection  is  as  follows  :  If  the  lines  in 
the  spectrum  are  due  to  the  vibrations  of  the  corpuscles  in 
the  atom,  then  since  for  n  corpuscles  there  are  3n  degrees 
of  freedom,  the  maximum  number  of  different  periods  of 
vibration  of  the  system,  i.e.,  of  lines  in  the  spectrum,  is  3n. 
Hence  on  this  view  the  number  of  corpuscles  in  the  atom 
could  not  be  less  than  one-third  the  number  of  lines  in  the 
spectrum,  and  this  would  for  many  elements  be  very  much 
greater  than  the  number  representing  the  atomic  weight. 
The  case  is,  however,  even  stronger  than  this,  for  all,  or 
nearly  all,  the  lines  in  the  line  spectra  of  the  elements  show 
the  Zeeman  effect,  i.e.,  they  can  be  resolved  by  a  magnetic 
field  into  at  least  three  components;  thus  each  line  showing 
this  effect  must  correspond,  not  to  a  single  isolated  period, 
but  to  the  coalescence  of  three  equal  periods.  Now  if  we 
consider  the  theory  of  the  vibrations  of  a  system  of  n  cor- 
puscles, we  find  that  p*,  where  p  is  the  frequency  of  a  vibra- 
tion, is  given  by  an  equation  of  the  3n  degree,  which  could 
have  at  most  3n  different  roots.  Many  of  these  roots,  how- 
ever, would  be  isolated  and  the  lines  in  the  spectrum 
corresponding  to  them  would  not  show  the  Zeeman  effect ; 
it  is  only  the  comparatively  small  number  of  frequencies,  for 
which  three  of  the  roots  of  the  equation  are  equal,  which 
would  give  rise  to  lines  having  the  properties  of  the  lines 
in  the  spectrum.  Thus  if  the  spectrum  of  a  body  arose 
from  the  vibrations  of  the  corpuscles  in  the  atoms  the 
number  of  corpuscles  would  have  to  be  very  greatly  in  excess 


NUMBEK   OF   CORPUSCLES   IN   AN   ATOM.    157 

of  the  number  of  lines  in  the  spectrum,  and  therefore  very 
much  larger  than  the  atomic  weight. 

I  would  urge  against  this  objection  that  we  have  no 
evidence  that  the  majority  of  the  lines  in  the  spectrum 
of  an  element  arise  from  the  atoms  when  in  the  normal 
state.  Luminosity  occurs  when  a  gas  is  either  traversed 
by  an  electric  current  or  when  it  is  raised  to  a  high  tem- 
perature, and  in  either  case  the  gas  is  ionized,  i.e.,  we  have, 
in  addition  to  the  normal  atoms,  positively  charged  ions 
and  negatively  electrified  corpuscles.  A  positively  electrified 
ion  and  a  corpuscle  might  form  a  system  analogous  to  the 
solar  system,  in  which  the  positively  electrified  ion,  with  its 
large  mass,  takes  the  part  of  the  sun  while  the  corpuscles 
circulate  round  it  as  planets.  The  forces  acting  on  the 
corpuscles  are  in  part  due  to  the  attraction  of  the  positive 
charge  which  produces  a  force  varying  inversely  as  the 
square  of  the  distance,  and  in  part  due  to  the  forces  arising 
from  the  corpuscles  and  positive  electricity  within  the  ion. 
Thus,  except  in  the  case  where  there  is  a  single  corpuscle  at 
the  centre  of  a  sphere  of  positive  electrification,  these  forces 
will  be  finite  and  will  vary  not  only  with  the  distance  of 
the  corpuscle  from  the  ion  but  also  with  the  angular 
position  of  the  corpuscle. 

Now  the  question  arises  whether  such  a  system  could 
give  rise  to  vibrations  having  definite  periods  separated 
by  finite  intervals  as  in  the  case  of  the  line  spectrum  of 
the  gas.  In  order  that  the  corpuscle  outside  the  ion  may 
give  a  definite  line  it  must  revolve  in  a  closed  orbit;  if 
orbits  having  all  possible  periods  within  certain  limits  were 
possible,  then  the  systems  of  ions  and  corpuscles  would 
give  a  continuous  and  not  a  line  spectrum.  Now  if  the 
forces  between  the  positive  ion  and  the  corpuscle  were 
simply  a  central  force  varying  inversely  as  the  square  of 
the  distance,  there  would  be  an  infinite  number  of  elliptic 
orbits  for  the  corpuscle  with  continuously  varying  periods, 
and  the  spectrum  would  be  a  continuous  one.  When,  how- 
ever, as  in  our  case,  the  force  between  the  ion  and  the  cor- 
puscle is  much  more  complex,  the  number  of  possible 


158     THE    CORPUSCULAR   THEORY  OE   MATTER. 

periodic  orbits  becomes  much  more  limited.  For  some  laws 
of  force  no  periodic  orbits  at  all  exist;  this,  for  example,  is 
the  case  where  the  total  force  on  the  corpuscle  is  that  due 
to  a  simple  electrical  doublet. 

The  results  obtained  by  Sir  George  Darwin  in  his  paper 
on  "  Periodic  Orbits  "  in  the  Acta-Mathematica  have  an  im- 
portant bearing  on  the  question  we  are  discussing.  Darwin 
discusses  the  possible  periodic  orbits  of  a  particle  of  infini- 
tesimal mass  under  the  action  of  the  sun  and  a  planet 


FIG.   28. 

whose  mass  is  1/10  that  of  the  sun.  If  we  consider  the 
orbits  in  which  the  particle  moves  as  a  satellite  round  the 
planet,  the  forces  acting  on  the  particle  will  consist  of  a 
central  force  varying  inversely  as  the  square  of  the  distance 
and  a  force  due  to  the  attraction  of  the  sun.  We  can  resolve 
this  force  into  two  forces,  one  acting  towards  the  planet  and 
the  other  at  right  angles  to  the  line  joining  the  planet  with 
its  satellite,  and  we  get  some  resemblance  between  these 
forces  and  those  on  a  corpuscle  arising  from  a  very  simple 
atom  with  a  positive  charge.  The  radial  attraction  due  to  the 
positive  charge  corresponds  to  the  attraction  of  the  planet, 


NUMBEK  OF   COEPUSCLES   IN   AN   ATOM.    159 

while  the  forces  due  to  the  corpuscles  and  sphere  of  positive 
electrification,  though  probably  much  more  complex,  may 
be  compared  with  the  attraction  of  the  sun. 

Now  Darwin  found  that  in  the  neighbourhood  of  the  planet 
there  is  a  region  (unshaded  area  6,  Fig.  28)  through  which 
no  periodic  orbit  can  pass,  and  though  with  the  proportion 
between  the  masses  of  the  sun  and  planet  of  10  to  1,  the 
region  is  not  closed,  Darwin  expresses  the  opinion  that  with 
a  larger  value  of  this  ratio  this  space  would  extend  to  an 
annular  ring  round  the  planet.  We  may,  perhaps,  imitate 
the  greater  complexity  of  the  forces  exerted  by  the  atom 
over  those  at  work  in  Darwin's  problem  by  supposing  that 
not  one  but  several  suns  disturb  the  motion  of  the  satellite  ; 
when  it  seems  not  improbable  that  we  might  have  several 
rings  instead  of  one  in  which  periodic  orbits  are  impossible. 
If  these  rings  grow  we  might  get  to  a  condition  of  things 
in  which  the  paths  of  periodic  orbits  are  confined  to  a 
number  of  annuli  (1),  (2)...(w),  between  these  rings.  If  the 
times  of  describing  the  orbits  in  region  (1)  vary  from  TI  to 
Ti  +  A  TI,  those  in  the  region  (2)  from  T2  to  T2  +  A  T2, 
and  so  on,  the  lines  in  the  spectrum  given  out  by  systems 
formed  by  the  positive  ion  and  one  corpuscle,  wo  aid  consist 
of  a  line  of  finite  width  corresponding  to  periods  of  vibration 
varying  from  TI  to  TI  +  A  TI,  followed  by  another  line 
with  periods  from  T2  to  T2  +  A  T2,  and  so  on:  if  A  Ti/Ti, 
A  TZ/TZ  are  small  these  lines  will  be  sharp,  while  if  these 
quantities  are  appreciable  the  lines  will  be  broad.  On  this 
view  the  different  lines  are  given  out  by  different  systems, 
the  line  TI  by  a  positive  ion  and  a  corpuscle  travelling 
round  the  region  (1),  the  line  T2  by  a  positive  ion  and  a  cor- 
puscle travelling  round  the  region  (2).  If  there  were  two 
corpuscles  travelling  round  the  same  ion,  one  corpuscle 
being  in  region  (1)  the  other  in  region  (2),  the  two  corpuscles 
would  repel  each  other  and  soon  make  the  orbits  very 
irregular.  The  very  large  variations  that  take  place  in  the 
relative  intensities  of  different  lines  in  the  spectra  produced 
by  electrical  discharges,  by  slight  alterations  in  the  discharge 
seem  in  accordance  with  the  view  that  the  different  lines 


160    THE    CORPUSCULAR   THEORY   OF   MATTER. 

originate  in  different  systems.  The  periods  T\  T2...are  deter- 
minate if  we  know  the  law  of  force  exerted  by  the  ion ;  the 
values  will  be  connected  with  each  other  by  certain  relations : 
in  other  words,  the  vibrations  corresponding  to  T\,  TV  •  •  would 
form  what  is  called  in  spectroscopy  a  series.  If  we  had  an 
ion  with  a  charge  of  two  units  of  electricity  instead  of  one, 


FIG.  29, 

the  regions  (1)  (2)... would  be  displaced  and  the  times  TI, 
T2)...  altered,  so  that  we  should  get  a  new  series. 

Any  line  arising  from  the  revolution  of  a  corpuscle  in 
a  closed  orbit  would  show  the  Zeeman  effect. 

Another  way  of  regarding  the  problem  which  leads  to 
similar  results  is  as  follows : — Suppose  we  regard  the  charged 
ion  as  a  Boscovichian  atom  exerting  a  central  force  on  a 
corpuscle  which  changes  from  repulsion  to  attraction  and 
from  attraction  to  repulsion  several  times  between  the 


NUMBER   OF   CORPUSCLES   IN   AN   ATOM.    161 

surface  of  the  ion  and  a  point  at  a  distance  from  the  surface 
comparable  with  molecular  distance,  such  a  force,  for 
example,  as  is  represented  graphically  in  Fig.  (29)  where 
the  abscissae  represent  distances  from  the  atom,  and  the 
ordinates  the  forces  exerted  by  the  atom  on  a  corpuscle  at  a 
distance  represented  by  the  abscissa,  the  forces  being 
repulsions  when  the  representative  point  is  below  the  line, 
attractions  when  it  is  above  it.  Now  from  any  point  where 
the  force  is  attractive  it  is  possible  to  project  a  corpuscle  at 
right  angles  to  the  radius  with  such  a  velocity  that  it  will, 
if  free  from  disturbance,  describe  a  circular  orbit  round  the 
atom.  The  theory  of  central  orbits  shows,  however,  that 
only  under  a  certain  condition  would  these  orbits  be  stable 
and  able  to  exist  in  a  system  like  that  in  a  luminous  gas 
subject  to  external  disturbances.  The  condition  that  the 
circular  orbit  should  be  stable  when  its  radius  is  a  is  that 
if  P,  the  central  attractive  force  due  to  the  atom  at  a 
distance  r,  is  written  in  the  form  P  =  u2  <£  (u),  where 
u  =  l/r,  then 

must  be  less  than  unity. 


(f)(a)  da 

Now  this  condition  will  only  be  satisfied  at  parts  of  the 
Boscovichian  curve  ;  if  these  parts  are  denoted  by  the 
thickened  portions  of  the  curve  in  Fig.  29,  the  possible 
orbits  will  be  confined  to  distances  from  the  atom  corre- 
sponding to  the  dotted  belts  in  the  figure,  and  we  shall 
get  the  same  conditions  as  before  and  the  same  arguments 
will  apply. 

It  might  be  urged  against  the  view  that  the  vibrations 
in  the  line  spectra  of  the  elements  are  due  to  systems 
manufactured  in  the  flame  or  in  the  electric  discharge,  and 
which  do  not  exist  in  the  normal  atom,  that  the  reversals 
of  the  bright  lines  in  a  spectrum  show  that  in  the  reversing 
layer  there  are  systems  which  have  the  same  periods  as 
those  producing  the  lines,  and  therefore  if  the  reversing 
layer  consists  of  gas  in  its  normal  state  there  must  in  such 
a  gas  be  systems  having  the  same  periods  of  vibration  as 

T.M.  M 


162  THE  CORPUSCULAR  THEORY  OF  MATTER. 

the  lines  in  the  spectrum.  It  must,  however,  be  remembered 
that  in" at  any  rate  the  great  majority  of  cases  the  reversing 
layer  does  not  consist  of  gas  in  its  normal  state ;  this  layer 
is  in  the  immediate  neighbourhood  of  the  luminous  gas  in 
the  arc,  spark  or  flame,  or  is  itself  at  a  high  temperature. 
In  all  these  cases  it  is  ionised,  i.e.,  contains  positive  ions 
and  corpuscles  which  may  build  up  a  system  like  those 
which  we  have  supposed  to  be  the  origin  of  the  bright  lines, 
and  absorb  the  light  having  the  same  period  as  those 
lines. 

ON  THE  ORIGIN  OF  THE  MASS  OF  THE  ATOM. 

Since  the  mass  of  a  corpuscle  is  only  about  one- seventeen- 
hundredth  part  of  that  of  an  atom  of  hydrogen,  it  follows 
that  if  there  are  only  a  few  corpuscles  in  the  hydrogen 
atom  the  mass  of  the  atom  must  in  the  main  be  due  to  its 
other  constituent — the  positive  electricity.  Now  we  have 
seen  that  the  mass  of  the  corpuscle  may  be  regarded  as 
arising  wholly  from  its  charge,  and  it  might  appear  that 
this  result  obliged  us  to  regard  mass  as  arising  in  two 
distinct  ways,  the  origin  of  one  kind  of  mass — that  of  the 
corpuscles — being  electrical,  while  that  of  the  rest  of  the 
atom  is  mechanical.  It  is,  however,  I  think,  possible  to 
take  a  point  of  view  from  which  this  separation  of  the 
nature  of  these  two  masses  disappears.  In  my  "Electricity 
and  Matter  "  (p.  6)  I  showed  that  we  might  regard  the  mass 
of  a  corpuscle  as  the  mass  of  the  ether  carried  along  by 
the  tubes  of  electric  force  attached  to  the  corpuscle  as  they 
move  through  the  ether.  An  example  taken  from  vortex 
motion  through  a  fluid  may  make  this  idea  clearer.  When 
a  vortex  ring  moves  through  the  fluid  it  carries  along  with 
it  a  volume  of  the  fluid  which  may  be  very  much  greater 
than  the  volume  of  the  ring  itself ;  in  fact,  if  the  ring  is 
very  thin  and  the  velocity  very  great,  the  volume  of  the 
ring  will  be  quite  insignificant  with  that  of  the  fluid  which 
it  carries  along  with  it.  Now  the  effective  mass  of  the  ring 
will  be  the  mass  of  the  ring  itself  plus  the  mass  of  the 
fluid  it  carries  with  it,  and  when  the  ring  is  thin  the 


NUMBEK   OF   COKPUSCLES   IN   AN   ATOM.     163 

effective  mass  will  be  practically  that  of  the  attached 
fluid.  The  ring  is  a  closed  curve  without  ends.  Let  us 
consider  the  case  of  a  vortex  filament  which  is  not  closed 
but  which  has  ends.  The  theory  of  vortex  motion  teaches 
us  that  these  ends  must,  if  they  are  not  on  the  free  surface 
of  the  liquid,  be  on  bodies  or  cavities  in  the  liquid.  Let  us 
suppose  that  the  ends  are  on  two  bodies,  A  and  B,  which 
are  so  light  as  to  have  no  appreciable  mass  of  their  own. 
Now  when  the  system  consisting  of  A  and  B  and  the  con- 
necting vortex  filament  moves  through  the  fluid  it  will 
carry  with  it  a  certain  volume  of  the  fluid,  and  if  the  fila- 
ment is  very  thin  the  effective  mass  of  the  system  will  be  the 
mass  of  this  fluid  carried  along  with  it  by  the  system.  Now 
this  fluid  is  carried  (1)  by  the  vortex  filament ;  (2)  by  the 
bodies  A  and  B  ;  if,  for  example,  the  latter  are  spheres, 
they  will  each  carry  along  with  them  a  volume  of  the  fluid 
amounting  to  one-half  of  their  own  volume.  Let  us  com- 
pare this  system  with  that  of  a  unit  of  positive  electricity 
connected  by  tubes  of  electric  force  with  a  unit  of  negative 
electricity,  the  tubes  of  electric  force  corresponding  to  the 
vortex  filament  and  the  seat  of  the  positive  and  negative 
electrification  to  the  bodies  A  and  B.  We  may  suppose 
that  when  this  system  moves  through  the  ether  it  carries 
some  of  the  ether  along  with  it ;  the  portion  carried  by  the 
tubes  of  force  will  depend  on  the  distribution  of  these  tubes, 
and  since  this  distribution  depends  on  the  velocity,  the 
mass  of  the  ether  carried  along  in  this  way  will  depend 
upon  the  velocity ;  the  portions  of  the  ether  carried  by  the 
seats  of  the  electrification  will,  if  our  analogy  holds,  not 
depend  upon  the  velocity.  We  may  interpret  the  results  of 
the  experiments  described  on  page  33  as  indicating  that  the 
amount  of  the  ether  carried  by  the  seat  of  the  negative 
electrification  is  very  small  compared  with  that  carried  by 
the  tubes  of  electric  force,  and  the  result  that  the  mass  of 
the  positive  electricity  is  large  compared  with  that  of  the  cor- 
puscle as  indicating  that  the  amount  of  ether  carried  along 
by  the  seat  of  the  positive  electricity  is  very  large  compared 
with  that  carried  by  the  tubes  of  electric  force  and  the  seat 


164    THE   CORPUSCULAR  THEORY  OF   MATTER. 

of  the  negative  electricity ;  that,  in  fact,  the  system  of  the 
positive  and  negative  units  of  electricity  is  analogous  to  a 
large  sphere  connected  with  vortex  filaments  with  a  very 
small  one,  the  large  sphere  corresponding  to  the  positive 
electrification,  the  small  one  to  the  negative. 

ON     THE     SlZE     OF     THE     SPHERE     OF     POSITIVE 

ELECTRIFICATION. 

The  connection  between  the  volume  of  the  sphere  of 
positive  electrification  and  the  number  of  corpuscles  in  the 
atom  is  a  very  important  question  on  the  theory  of  the 
structure  of  the  atom  which  we  have  been  discussing. 
The  number  of  corpuscles  in  the  atom  is  equal  to  the 
number  of  units  of  positive  electricity  in  the  sphere,  and  is 
proportional  to  the  atomic  weight. 

The  great  majority  of  the  methods  by  which  the  size  of 
atoms  is  determined  do  not  give  the  geometrical  boundary 
of  the  atom,  but  what  is  called  the  range  of  molecular 
action,  i.e.,  the  greatest  distance  at  which  the  forces  due 
to  the  atom  produce  appreciable  effect ;  they  give,  in  fact, 
the  dynamical  rather  than  the  geometrical  boundary  of  the 
atom.  On  a  theory  such  as  that  of  Boscovich,  in  which  the 
atoms  are  regarded  merely  as  centres  of  force,  the  dynamical 
boundary  is  the  only  one  which  has  to  be  considered  ;  but 
in  a  theory  such  as  the  one  we  have  been  discussing,  where 
we  regard  the  atom  as  having  a  definite  size  and  shape,  we 
have  to  consider  the  geometrical  as  well  as  the  dynamical 
boundary  of  the  atom. 

There  is  one  method,  however,  by  which  we  can  in  certain 
cases  deduce  the  geometrical  boundary  of  the  atom,  for  we 
have  seen  that  for  a  monatomic  gas,  if  ft  is  the  refractive 
index  for  infinitely  long  waves — 

=  N  a3 

where  a  is  the  radius  of  the  sphere  of  positive  electrification 
and  N  the  number  of  atoms  per  unit  volume  of  the  gas. 


NUMBER  OF  CORPUSCLES  IN  AN  ATOM.  165 
For  a  gas  //,  is  so  nearly  equal  to  unity  that  we  may  write 
-  (p  —  1)  for'*^--,  so  that  for  gases  M  -  1  will  be  pro- 
portional to  the  volume  of  the  sphere  of  positive  electrifica- 
tion. The  following  Table,  the  data  for  which  are  taken 
from  the  paper  by  Cuthbertson  and  Metcalfe  (Phil.  Trans., 
A.,  vol.  207,  p.  138, 1907),  gives  the  value  of  /*  —  1  for  many 
of  the  elements  when  in  the  gaseous  state : — 


Gas. 

M-5- 

Atomic 
weight. 

10«x(/i-  l)/(atoraic 

weight). 

Helium  .     . 

72  X  10-6 

4 

18 

Neon      .     . 

137  X  10~6 

20 

6-85 

Argon    .     . 

508  X  10-6 

40 

12-7 

Krypton 

850  X  10~6 

80 

10-6 

Xenon    .     . 

1378  X  10-6 

128 

10-7 

Mercury 

1866  X  10-6 

200 

9-3 

Hydrogen  . 

139  X  10-6 

1 

139 

(  Nitrogen     . 

297  X  10-6 

14 

21 

-  Phosphorus 

1197  X  10-6 

31 

39 

(  Arsenic 

1550  X  10-6 

75 

20 

/  Oxygen       . 
1  Sulphur     . 

270  X  10-6 
1101  x  10-6 

16 
82 

17 
34 

1  Selenium   . 

1565  X  10-6 

79 

20 

(Tellurium  . 

2495  X  10-6 

127 

20 

(Zinc       .     . 

2060  X  10-  6 

65 

30 

i  Cadmium  . 

2675  X  10-6 

112 

24 

For  the  lighter  elements  the  variations  in  (/*-!)/  (atomic 
weight)  are  very  irregular,  but  for  those  of  large  atomic 
weight  in  one  group  this  quantity  is  fairly  constant,  indi- 
cating that  the  volume  of  the  sphere  of  positive  electrification 
is  roughly  proportional  to  the  atomic  weight  when  there  are 
a  great  many  corpuscles  in  the  atom. 

In  many  compounds  of  the  lighter  elements  the  value  of 


T.M. 


M1 


166  THE  CORPUSCULAR  THEORY  OF  MATTER. 

(/A  — 1)  does  not  increase  nearly  as  rapidly  as  the  density, 
and  for  a  considerable  number  of  such  compounds  the  value 
Of  (yx.— 1)  at  constant  temperature  and  pressure  is,  as  Traube 
has  shown,  approximately  proportional  to  the  sum  of  the 
valencies  of  the  atoms  in  a  molecule  of  the  compound. 
The  preceding  table  shows  that  this  result  does  not  apply 
to  the  heavier  elements. 

We  may  illustrate  the  effect  of  valency  on  the  refractive 
index  in  the  following  way  : — We  have  supposed  that  there 
are  in  the  atom  some  corpuscles  equal  in  number  to  the 
valency  which  are  especially  easily  moved.  To  represent 
the  mobility  of  these  corpuscles  let  us  suppose  that  they 
are  placed  in  a  shell  of  positive  electricity  of  small  density 
around  the  much  denser  core  which  contains  the  rest  of  the 
corpuscles  and  the  equivalent  quantity  of  positive  electricity. 
Thus  we  may  picture  the  atom  as  having  a  crowded  centre, 
surrounded  by  a  rarified  atmosphere  through  which  a  few 
corpuscles  are  scattered,  the  positive  electricity  in  the 
atmosphere  being  equivalent  to  the  negative  charge  on  the 
corpuscles  scattered  through  it. 

Now  we  can  easily  see  that  the  value  of  (^  —  1)  for  a 
collection  of  atoms  of  this  kind  will  consist  of  two  terms, 
one  proportional  to  the  volume  of  the  atmosphere,  and  the 
other  proportional  to  the  volume  of  the  core.  The  volume 
of  the  atmosphere  will  be  proportional  to  the  number  of 
corpuscles  in  it,  i.e.,  to  the  positive  valency,  while  the 
volume  of  the  core  will  be  proportional  to  the  number  of 
the  remaining  corpuscles ;  this  for  elements  whose  atomic 
weight  is  large  compared  with  their  valency,  will  be  pro- 
portional to  the  atomic  weight. 

Thus,  the  value  of  (/*—!)  will  consist  of  two  terms,  one 
proportional  to  the  valency,  the  other  to  the  atomic  weight. 
When  the  atomic  weight  is  not  great  the  first  term  may  be 
the  important  one,  while  for  the  heavier  elements  the 
effect  of  the  atomic  weight  may  overpower  that  of  the 
valency. 

The  dispersion  of  the  substance  is  influenced  by  the 
valency  atoms  to  an  even  greater  extent  than  the  refractivity 


NUMBEE   OF   COKPUSCLES   IN    AN   ATOM.    167 

for  we   can   show  that  /*,  the   refractive  index  for  waves. 
of  length  A,  is  given  by  the  equation 

/A2      -    1  p     j_    p  2     m  1    STT 

V  +  2  r  '   A?"    ?I~A* 


where  .Y  is  the  number  of  atoms  per  cubic  centimetre,. 
m  and  e  the  mass  and  charge  of  a  corpuscle,  P0  the  part  of 
(/A2—  1)  /  (/x2  +  2)  due  to  the  core  for  infinitely  long  waves,  Q0. 
the  part  due  to  the  atmosphere,  n  the  number  of  corpuscles 
in  the  core,  p  the  number  of  valency  corpuscles.  Since  p  is  in 
general  small  compared  with  //,  we  see  that  unless  P0  is 
large  compared  with  Q0,  the  part  of  the  co-efficient  of  1/A2; 
which  depends  on  Q0  will  be  much  larger  than  that  which 
depends  on  P0,  i.e.,  the  dispersion  will  depend  chiefly  on 
the  valency  atoms. 

As  these  valency  atoms  are  easily  detached  we  should 
expect  that  they  would  increase  the  amount  of  ionization 
when  the  gas  is  ionized  by  some  external  means.  Bragg; 
finds  that  the  number  of  ions  produced  by  the  a  rays- 
from  radium  in  equal  volumes  of  different  gases  at  the 
same  temperature  and  pressure  is  proportional  to  the 
molecular  volume  of  the  gas.  As  this  molecular  volume  is- 
proportional  to  (/*  —  1),  and  as  the  valency  corpuscles  have 
great  influence  on  this  quantity  for  the  lighter  elements,  we- 
see  that  thev  also  increase  the  ionization. 


INDEX. 


A. 

o  PARTICLES,  properties  of,  25 

value  of  e/m  for,  24 
Abegg,  on  valency,  118 
Absorption  of  cathode  rays,  148, 

150 
Alloys,    thermal    and    electrical 

conductivity  of,  58,  59 
Anomalous  dispersion,  137 
Arrangement    of     corpuscles    in 

atom,  103  et  seq. 
Atom,  Boscovichian,  160 

number  of  corpuscles  in, 

142  et  seq. 

origin  of  mass  of,  162 
volume  of,  164 
Atoms,  forces  between,  120 

forces  between  like  atoms 

in  a  molecule,  127 
Attraction,  residual,  137 

B. 
BARKLA,     energy     of     secondary 

radiation,  144,  147 
Becker,    absorption    of    cathode 

rays,  150 
Becquerel,  velocity  of  ft  rays  from 

uranium,  150 
Bonds,  chemical,  136 
Boscovichian  atom,  160 
Bose,  effect  of  electric  charge  on 

electric  resistance  of  a  metal,  83 
Boyle's    law,    interpretation     of 

deviations  from,  136 
Bragg,  properties  of  a  particles, 

25 


C. 

CANALSTRAHLEN,  17 

spectrum  produced  by,  18 
value  of  ejm  for,  18  et  seq. 
Carbon  atom,  133,  134 
Cathode  rays, 

absorption  of,  148,  150 
determination  of  velocity  of,  8 
electrostatic  deflection  of,  5 
magnetic  deflection  of,  7 
penetration  of,  Hertz  experi- 
ments, 7 
Charge     of    negative     electricity 

carried  by  cathode  rays,  4 
Chemical  combination,  120 
Combination,  chemical,  120 
Condensation  of  water  drops,  11 
Conduction,  electric,  corpuscular 

theory  of,  49,  86 
Conduction  metallic,  corpuscular 

theory  of,  49  et  seq. 
Conduction  thermal,  corpuscular 

theory  of,  55,  88 

Corpuscle,  electric  field  due  to,  44 
magnetic  field  due  to,  44 
origin  of  mass  of,  28 
Corpuscles> 

arrangement  in  one  plane,  107 

definition  of  2 

electric  charge  carried  by,  11 

mass  of,  16 

number  in  an  atom,  142  et  seq. 

number  of  per  unit  volume  of 

a  metal,  80 

occurrence  of,  10 

Corpuscular  pressure,  119 


170 


INDEX. 


Corpuscular     theory,     statement 

of,  1 

theory  of  radiation,  61  et  seq. 
Crookes,  Sir  W.,  experiment  with 

cathode  rays,  3 

Cuthbertson  and  Metcalfe,  refrac- 
tivity  of  gases,  165 

D. 

DARWIN,  SIR  G.,  periodic  orbits, 
158 

Deflection  of  cathode  rays 
by  an  electric  field,  5 
by  a  magnetic  field,  7 
Des  Coudres,  value  of  elm  for  a 

particles,  24 

Dewar    and    Fleming,    effect    of 
temperature   on    resistance   of 
metals  and  alloys,  59 
Diesselhorst  and  Jaeger,  electric 
and  thermal  conductivities,  57 
Dispersion,  anomalous,  137 
Dispersion  of  light,  152 

influence  of  valency  on,  155 
Drude,  anomalous  dispersion,  137 
effect  of  valency  on  disper- 
sion, 155 

E. 

ELECTRIC  charge  carried  by  a  cor- 
puscle, 11 
conduction,  corpuscular 

theory  of,  49,  86 
field  due  to  corpuscles, 

44 

force,  tubes  of,  138 
Electricity,  one  fluid  theory  of,  26 
Electrolysis  of  bromine  and  iodine 

solutions,  130 

Electropositive  and  electronega- 
tive elements,  114 

valency,  117,  122 
Electrostatic  deflection  of  cathode 

rays,  5 
#lm  values  for  a  particles,  24 


elm  values  for  canalstrahlen,  18  et 

seq. 

corpuscles,  32 
Ethane,  131 
Ethylene,  132 

F. 

FITZGERALD,  Peltier  effect,  76 
Fleming  and  Dewar,  effect  of  tem- 
perature on  resistance  of  metals 
and  alloys,  59 
Floating    magnets,    arrangement 

of,  110 

Force,  tubes  of,  138 
Forces  between  atoms,  120 

between    like     atoms    in 

molecule,  127 

Fourier,  analysis  of  radiation,  65, 
91 

G. 

GASES,  refractivity  of,  165 
Goldstein,  canalstrahlen,  17 

H. 

HAGEN  and  llubens,  electric  con- 
ductivity of  metals,  84 

Hall  effect,  68,  99 

Helium,  canalstrahlen  in,  21 

Hertz,    penetration    of     cathode 
rays,  7 

Huff,  value  of  e\m  for  a  particles, 
24 

Hydrogen,  canalstrahlen  in,  21 
dispersion  of,  153 

I. 

IONS,  velocity  of,  139 

Iron  salts,  magnetism  of,  141 

Isomers,  131 

J. 

JAEGER  and  Diesselhorst,  electric 
and  thermal  conductivities,  57 


INDEX. 


171 


K. 
KAUFMANN,    values    of     ejm    for 

rapidly  moving  corpuscles,  32 
Ketteler,  formula  for  dispersion, 

153 
Kelvin,  forces  between  electrified 

systems,  121 
Kleeman,  properties  of  a  particles, 

25 

L. 

LARMOR,  radiation  from  moving 

corpuscle,  91 
Light,  dispersion  of,  153 
Lorentz,  formula  for  dispersion  of 

light,  153 

theory  of  radiation,  61 
Zeeman  effect,  35 

M. 
MACKENZIE,   value   of  efm  for  a 

particles,  24 
Magnetic    deflection   of    cathode 

rays,  7 

force   due   to   moving 

corpuscles,  43 

effect  of,  on  flow 

of  a  current,  68 

Magnetism  of  iron  salts,  141 

oxygen,  140 
Magnets,  arrangement  of  floating, 

110 
Mass  of  atom,  origin  of,  162 

corpuscle,  origin  of,  28 
Mayer,  experiments  with  floating 

magnets,  110 
Mercury  vapour,  conductivity  of, 

50 
Minarelli,  thermo-electric  effects, 

76 
Metcalfe    and    Cuthbertson,    re- 

fractivity  of  gases,  165 
Molecule,  forces  between  atoms 

in,  127 

Monckman,     experiments     with 
floating  electrified  bodies,  112 


N. 

NUMBER  of  corpuscles 

in  an  atom,  142  et  seq. 
per  unit  volume  of  a  metal, 
80 


0. 

OBERMAYER,        thermoelectric 

effects,  76 
Orbits  periodic,  157 
Origin  of  spectra,  157 
Oxygen,  magnetism  of,  140 


P. 

PELTIER   difference  of  potential,. 

73,  97 

Periodic  orbits,  157 
Perrin,  negative  charge  carried  by 

cathode  rays, 
Positive  electricity,  17 
from  hot  wires,  23 
from  radioactive  substances^ 

24 

size  of  sphere  of,  164 
Pressure,  corpuscular,  119 
Pulses  produced  by  stopping  and 
starting  corpuscles,  45 


E. 


EADIATION,  corpuscular  theory  of , 

61 

Kadicles  organic,  134 
Kayleigh  (Lord),  92 

conductivity  of  alloys,  59 
Eefractivity  of  gases,  165 
Eesistance,    effect    of    magnetic 

field  on  electrical,  101 
Eeversal  of  lines  in  spectra,  161 
Eontgen  radiation,  secondary,  142 
Eontgen  rays,  theory  of,  47 


172 


INDEX. 


Eubens  and  Hagen,  conductivity 

of  metals,  84 
Rutherford,   value   of   efm   for   a 

particles,  24 


S. 


SATURATED  compounds,  135 
Schulze,  thermal  and  electric  con- 
ductivity, 58 

Secondary  Eontgen  radiation,  142 
Size  of  sphere  of  positive  electri- 
fication, 164 
Spectrum,  origin  of,  157 

produced     by     canal- 

strahlen,  18 
reversal  of  lines  in,  161 
Sphere  of  uniform  positive  elec- 
trification, 164 
Stokes  (Sir  G.  G.), 

energy      due     to      a      sphere 

moving  in  water,  29 
velocity  of  falling  drops,  14 
Strutt,  conductivity   of  mercury 
vapour,  50 


T. 


THERMAL    conductivity,    corpus- 

culai  theory  of,  55,  88 
Thomson  effect,  76,  97 
Townsend,    magnetism    of    iron 

salts,  141 

Traube,  volume  and  valency,  166 
Tubes  of  electric  force,  138 


U. 

UNSATURATED    compounds,    126, 
135 

V. 

VALENCY,  115  et  seq. 

corpuscles,  166 

positive   and   negative,  117 
Van  der  Waals  equation,  135 
Vant  Hoff,  organic  radicles,  134 
Velocity  of  ions,  139 
Volume  of  atom,  164 
Vortex  atom  theory  of  matter,  2 
motion,  analogy  with  elec- 
trical system,  162 

W. 

WALDEN,  electrolysis  of  bromine 
and  iodine  solutions, 
130 

on  valency,  118 

Wehnelt,  lime  coated  cathode,  6 
Wien  W.,  value  of  e/m  for  canal- 

strahlen,  18 
Wilson,  C.  T.  B.,  condensation  of 

water  drops,  11 
Wilson,  H.  A.,  measurement   of 

charge  on  drops,  15 
Wood,  experiments  with  floating 

magnets,  112 
Work    required    to    disintegrate 

atom,  104 

Z. 
ZEEMAN  effect,  34,  156 


BRADBURY,    AGNEW,    &   CO.    LD.,    PRINTERS,    LONDON  AND  TONBRIDGE. 

" 


RETURN  TO:      CIRCULATION  DEPARTMENT 
198  Main  Stacks 


LOAN  PERIOD     1 
Home  Use 

2 

3 

4 

5 

6 

ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS. 

Renewals  and  Recharges  may  be  made  4  days  prior  to  the  due 
date.  Books  may  be  renewed  by  calling  642-3405. 


DUE  AS  STAMPED  BELOW. 

Aiir  o  o  or 

f\f* 

AUtl    U  o  Zl 

06 

FORM  NO.  DD6                         UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
50  M    1-06                                                  Berkeley,  California  94720-6000 

PHYSICS  LIBRARY 

U.  C.  BERKELEY  LIBRARIES 


